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Some Spectral Properties of Uniform Hypergraphs

2014-10-30
Jiang Zhou , Lizhu Sun , Wenzhe Wang +1 more
For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the Laplacian tensor of $H$, which imply that $\sum_{i=1}^nd_i^s$ ($s=1,\ldots,k$) is determined by the Laplacian spectrum of $H$, where … For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the Laplacian tensor of $H$, which imply that $\sum_{i=1}^nd_i^s$ ($s=1,\ldots,k$) is determined by the Laplacian spectrum of $H$, where $d_1,\ldots,d_n$ is the degree sequence of $H$. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spectral characterizations of odd-bipartite hypergraphs, and give a partial answer to a question posed by Shao et al (2014). We also give some spectral properties of power hypergraphs, and show that a conjecture posed by Hu et al (2013) holds under certain conditons.
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The inverse, rank and product of tensors

2014-01-07
Changjiang Bu , Xu Zhang , Jiang Zhou +2 more

Some results on resistance distances and resistance matrices

2014-06-11
Lizhu Sun , Wenzhe Wang , Jiang Zhou +1 more
In this paper, we obtain formulas for resistance distances and Kirchhoff index of subdivision graphs. An application of resistance distances to the bipartiteness of graphs is given. We also give … In this paper, we obtain formulas for resistance distances and Kirchhoff index of subdivision graphs. An application of resistance distances to the bipartiteness of graphs is given. We also give an interlacing inequality for eigenvalues of the resistance matrix and the Laplacian matrix.

Resistance distance in subdivision-vertex join and subdivision-edge join of graphs

2014-06-28
Changjiang Bu , Bo Yan , Xiuqing Zhou +1 more

Brualdi-type eigenvalue inclusion sets of tensors

2015-05-16
Changjiang Bu , Yuanpeng Wei , Lizhu Sun +1 more

Resistance distance and Kirchhoff index of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" display="inline" overflow="scroll"><mml:mi>R</mml:mi></mml:math>-vertex join and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.gif" display="inline" overflow="scroll"><mml:mi>R</mml:mi></mml:math>-edge join of two graphs

2015-03-16
Xiaogang Liu , Jiang Zhou , Changjiang Bu

Morrey Spaces for Nonhomogeneous Metric Measure Spaces

2013-01-01
Yonghui Cao , Jiang Zhou
The authors give a definition of Morrey spaces for nonhomogeneous metric measure spaces and investigate the boundedness of some classical operators including maximal operator, fractional integral operator, and Marcinkiewicz integral … The authors give a definition of Morrey spaces for nonhomogeneous metric measure spaces and investigate the boundedness of some classical operators including maximal operator, fractional integral operator, and Marcinkiewicz integral operators.
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A note on block representations of the group inverse of Laplacian matrices

2012-01-01
Changjiang Bu , Lizhu Sun , Jiang Zhou +1 more
Let G be a weighted graph with Laplacian matrix L and signless Laplacian matrix Q.In this note, block representations for the group inverse of L and Q are given.The resistance … Let G be a weighted graph with Laplacian matrix L and signless Laplacian matrix Q.In this note, block representations for the group inverse of L and Q are given.The resistance distance in a graph can be obtained from the block representation of the group inverse of L.
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Group inverse for block matrices and some related sign analysis

2011-11-25
Jiang Zhou , Changjiang Bu , Yimin Wei
The sign pattern of a real matrix M is the (0, 1, −1)-matrix obtained from M by replacing each entry by its sign. Let N ∈ ℝ n×n be a … The sign pattern of a real matrix M is the (0, 1, −1)-matrix obtained from M by replacing each entry by its sign. Let N ∈ ℝ n×n be a group invertible matrix. Let Q(N) be the set of real matrices with the same sign pattern as N. For any , if is group invertible and the group inverses of N and have the same sign pattern, then N is called an S2GI matrix. In this article, we present the existence and the representations for the group inverse of some block matrices with one or two full rank sub-blocks, and give a family of block matrices which are S2GI matrices. Applying these results, we can partially determine the sign pattern of the solution of singular linear system with index one.

On the Resistance Matrix of a Graph

2016-03-04
Jiang Zhou , Zhongyu Wang , Changjiang Bu
Let $G$ be a connected graph of order $n$. The resistance matrix of $G$ is defined as $R_G=(r_{ij}(G))_{n\times n}$, where $r_{ij}(G)$ is the resistance distance between two vertices $i$ and … Let $G$ be a connected graph of order $n$. The resistance matrix of $G$ is defined as $R_G=(r_{ij}(G))_{n\times n}$, where $r_{ij}(G)$ is the resistance distance between two vertices $i$ and $j$ in $G$. Eigenvalues of $R_G$ are called R-eigenvalues of $G$. If all row sums of $R_G$ are equal, then $G$ is called resistance-regular. For any connected graph $G$, we show that $R_G$ determines the structure of $G$ up to isomorphism. Moreover, the structure of $G$ or the number of spanning trees of $G$ is determined by partial entries of $R_G$ under certain conditions. We give some characterizations of resistance-regular graphs and graphs with few distinct R-eigenvalues. For a connected regular graph $G$ with diameter at least $2$, we show that $G$ is strongly regular if and only if there exist $c_1,c_2$ such that $r_{ij}(G)=c_1$ for any adjacent vertices $i,j\in V(G)$, and $r_{ij}(G)=c_2$ for any non-adjacent vertices $i,j\in V(G)$.
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Laplacian spectral characterization of some graphs obtained by product operation

2012-02-25
Jiang Zhou , Changjiang Bu

The enumeration of spanning tree of weighted graphs

2020-08-17
Jiang Zhou , Changjiang Bu
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Signless Laplacian spectral characterization of the cones over some regular graphs

2012-01-14
Changjiang Bu , Jiang Zhou

Parabolic equations with VMO coefficients in generalized Morrey spaces

2010-01-01
Lin Zhang , Yin Sheng Jiang , Jiang Zhou

Starlike trees whose maximum degree exceed 4 are determined by their Q-spectra

2011-07-24
Changjiang Bu , Jiang Zhou

Some block matrices with signed Drazin inverses

2012-06-04
Jiang Zhou , Changjiang Bu , Yimin Wei

Some inequalities for the Hadamard product of tensors

2017-07-07
Lizhu Sun , Baodong Zheng , Jiang Zhou +1 more
Let and be two order m dimension n tensors. The Hadamard product is an order m dimension n tensor with entries . For nonnegative tensors and , we obtain some … Let and be two order m dimension n tensors. The Hadamard product is an order m dimension n tensor with entries . For nonnegative tensors and , we obtain some bounds on spectral radius of in terms of spectral radius and entries of and . We give some inequalities for the minimum eigenvalue and determinant of the Hadamard product involving M-tensors and Z-tensors, and use them to derive some criteria of M-tensors.

Resistance characterizations of equiarboreal graphs

2017-08-24
Jiang Zhou , Lizhu Sun , Changjiang Bu

Principal eigenvectors and spectral radii of uniform hypergraphs

2018-03-07
Haifeng Li , Jiang Zhou , Changjiang Bu

The boundedness of fractional integral operators in local and global mixed Morrey-type spaces

2022-02-01
Houkun Zhang , Jiang Zhou
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Spectral characterization of line graphs of starlike trees

2012-11-02
Jiang Zhou , Changjiang Bu
Two graphs are said to be A-cospectral if they have the same adjacency spectrum. A graph G is said to be determined by its adjacency spectrum if there is no … Two graphs are said to be A-cospectral if they have the same adjacency spectrum. A graph G is said to be determined by its adjacency spectrum if there is no other non-isomorphic graph A-cospectral with G. A tree is called starlike if it has exactly one vertex of degree greater than 2. In this article, we prove that the line graphs of starlike trees with maximum degree at least 12 are determined by their adjacency spectra.

A note on the multiplicities of graph eigenvalues

2013-08-30
Changjiang Bu , Xu Zhang , Jiang Zhou

Some characterizations of M-tensors via digraphs

2016-01-29
Jiang Zhou , Lizhu Sun , Yuanpeng Wei +1 more

Some Results for the Periodicity and Perfect State Transfer

2011-09-20
Jiang Zhou , Changjiang Bu , Jihong Shen
Let $G$ be a graph with adjacency matrix $A$, let $H(t)=\exp(itA)$. $G$ is called a periodic graph if there exists a time $\tau$ such that $H(\tau)$ is diagonal. If $u$ … Let $G$ be a graph with adjacency matrix $A$, let $H(t)=\exp(itA)$. $G$ is called a periodic graph if there exists a time $\tau$ such that $H(\tau)$ is diagonal. If $u$ and $v$ are distinct vertices in $G$, we say that perfect state transfer occurs from $u$ to $v$ if there exists a time $\tau$ such that $|H(\tau)_{u,v}|=1$. A necessary and sufficient condition for $G$ is periodic is given. We give the existence for the perfect state transfer between antipodal vertices in graphs with extreme diameter.

Some results on the Drazin inverse of anti-triangular matrices

2013-01-17
Changjiang Bu , Lizhu Sun , Jiang Zhou +1 more
AbstractAbstractThe representations for the Drazin inverse of anti-triangular matrices are obtained under some conditions. Applying these representations, we give a necessary condition for a class of block matrices to have … AbstractAbstractThe representations for the Drazin inverse of anti-triangular matrices are obtained under some conditions. Applying these representations, we give a necessary condition for a class of block matrices to have signed Drazin inverse.Keywords: Drazin inverseMP inversesign patternsigned Drazin inverseClassification: 15A0915B35 AcknowledgmentsThe authors would like to thank the referee for their valuable suggestions. J. Zhou is supported by the Fundamental Research Funds for the Central Universities. Y. Wei is supported by the National Natural Science Foundation of China under Grant 11271084, Doctoral Program of the Ministry of Education under Grant 20090071110003, Shanghai Science & Technology Committee and Shanghai Education Committee (Dawn Project).

Spectral Characterizations of the Corona of a Cycle and Two Isolated Vertices

2013-05-27
Changjiang Bu , Jiang Zhou , Hongbo Li +1 more

Error estimates for triangular and tetrahedral finite elements in combination with a trajectory approximation of the first derivatives for advection-diffusion equations

2011-10-01
Hongtao Chen , Qun Lin , Vladimir Shaĭdurov +1 more

Characterization of CMO via compactness of the commutators of bilinear fractional integral operators

2018-11-01
Dinghuai Wang , Jiang Zhou , Zhidong Teng
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Spectral determination of some chemical graphs

2012-01-01
Changjiang Bu , Jiang Zhou , Hongbo Li
Let Tk denote the caterpillar obtained by attaching k pendant edges at two pendant vertices of the path Pn and two pendant edges at the other vertices of Pn. It … Let Tk denote the caterpillar obtained by attaching k pendant edges at two pendant vertices of the path Pn and two pendant edges at the other vertices of Pn. It is proved that Tk is determined by its signless Laplacian spectrum when k = 2 or 3, while T2 by its Laplacian spectrum.
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Sharp estimates for the p-adic Hardy type operators on higher-dimensional product spaces

2017-09-12
Ronghui Liu , Jiang Zhou
In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic … In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spaces. Furthermore, the p-adic weighted Hardy-Cesàro operator is also obtained.
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Weighted multilinear p-adic Hardy operators and commutators

2017-12-29
Ronghui Liu , Jiang Zhou
Abstract In this paper, the weighted multilinear p -adic Hardy operators are introduced, and their sharp bounds are obtained on the product of p -adic Lebesgue spaces, and the product … Abstract In this paper, the weighted multilinear p -adic Hardy operators are introduced, and their sharp bounds are obtained on the product of p -adic Lebesgue spaces, and the product of p -adic central Morrey spaces, the product of p -adic Morrey spaces, respectively. Moreover, we establish the boundedness of commutators of the weighted multilinear p -adic Hardy operators on the product of p -adic central Morrey spaces. However, it’s worth mentioning that these results are different from that on Euclidean spaces due to the special structure of the p -adic fields.
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E-cospectral hypergraphs and some hypergraphs determined by their spectra

2014-08-02
Changjiang Bu , Jiang Zhou , Yimin Wei
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Spectral moments of hypertrees and their applications

2021-07-15
Lixiang Chen , Changjiang Bu , Jiang Zhou
The formula for the spectral moment of graphs which is represented by the number of subgraphs is called the RNS spectral moment formula of graphs. In this paper, the research … The formula for the spectral moment of graphs which is represented by the number of subgraphs is called the RNS spectral moment formula of graphs. In this paper, the research on the RNS spectral moment formula of graphs is generalized to hypergraphs. We give a formula for the spectral moment of a hypertree in terms of the number of some subhypertrees. Using this formula, we obtain the first 3k codegree coefficients of the characteristic polynomial of a k-uniform hypertree in terms of the number of some subhypertrees.

Line star sets for Laplacian eigenvalues

2013-11-21
Jiang Zhou , Lizhu Sun , Wenzhe Wang +1 more
Let G be a mixed graph with a nonzero Laplacian eigenvalue μ of multiplicity k. A line star set for μ in G is a set Y of k edges … Let G be a mixed graph with a nonzero Laplacian eigenvalue μ of multiplicity k. A line star set for μ in G is a set Y of k edges of G such that μ is not a Laplacian eigenvalue of G−Y. It is shown that line star set exists for any nonzero Laplacian eigenvalue of any mixed graph. Some basic properties for line star sets are given. We also obtain some results on line star sets in undirected graphs.

Lipschitz Spaces and Fractional Integral Operators Associated with Nonhomogeneous Metric Measure Spaces

2014-01-01
Jiang Zhou , Dinghuai Wang
The fractional operator on nonhomogeneous metric measure spaces is introduced, which is a bounded operator from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mfenced separators="|"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:mfenced></mml:math>into the space<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:msup><mml:mfenced separators="|"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:mfenced></mml:math>. Moreover, the Lipschitz spaces on nonhomogeneous … The fractional operator on nonhomogeneous metric measure spaces is introduced, which is a bounded operator from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mfenced separators="|"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:mfenced></mml:math>into the space<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:msup><mml:mfenced separators="|"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:mfenced></mml:math>. Moreover, the Lipschitz spaces on nonhomogeneous metric measure spaces are also introduced, which contain the classical Lipschitz spaces. The authors establish some equivalent characterizations for the Lipschitz spaces, and some results of the boundedness of fractional operator in Lipschitz spaces are also presented.
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Laplacian and signless Laplacian Z-eigenvalues of uniform hypergraphs

2015-03-25
Changjiang Bu , Fan Yamin , Jiang Zhou

Pseudodifferential operators with smooth symbols and their commutators on weighted Morrey spaces

2018-02-21
Xi Hu , Jiang Zhou

A Note on Campanato Spaces and Their Applications

2018-03-01
Dinghuai Wang , Jiang Zhou , Zhidong Teng

Anisotropic Herz-type Hardy spaces with variable exponent and their applications

2018-06-26
Hou Yu Zhao , Jiang Zhou

Inverse Perron Values and Connectivity of a Uniform Hypergraph

2018-11-02
Changjiang Bu , Haifeng Li , Jiang Zhou
In this paper, we show that a uniform hypergraph $\mathcal{G}$ is connected if and only if one of its inverse Perron values is larger than $0$. We give some bounds … In this paper, we show that a uniform hypergraph $\mathcal{G}$ is connected if and only if one of its inverse Perron values is larger than $0$. We give some bounds on the bipartition width, isoperimetric number and eccentricities of $\mathcal{G}$ in terms of inverse Perron values. By using the inverse Perron values, we give an estimation of the edge connectivity of a $2$-design, and determine the explicit edge connectivity of a symmetric design. Moreover, relations between the inverse Perron values and resistance distance of a connected graph are presented.
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Another characterizations of Muckenhoupt A p class

2017-09-29
Dinghuai Wang , Jiang Zhou , Wenyi Chen

Characterizations of Weighted BMO Space and Its Application

2021-08-01
Ding Huai Wang , Jiang Zhou , Zhi Dong Teng
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Blow-up for compressible Euler system with space-dependent damping in 1-D

2023-01-01
Jinbo Geng , N. Lai , Manwai Yuen +1 more
Abstract This article considers the Cauchy problem for compressible Euler system in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="bold">R</m:mi></m:math> {\bf{R}} with damping, in which the coefficient depends on the space variable. Assuming the initial … Abstract This article considers the Cauchy problem for compressible Euler system in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="bold">R</m:mi></m:math> {\bf{R}} with damping, in which the coefficient depends on the space variable. Assuming the initial density has a small perturbation around a constant state and both the small perturbation and the small initial velocity field are compact supported, finite-time blow-up result will be established. This result reveals the fact that if the space-dependent damping coefficient decays fast enough in the far field (belongs to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mrow><m:mi>L</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msup><m:mrow><m:mo>(</m:mo><m:mrow><m:mi mathvariant="bold">R</m:mi></m:mrow><m:mo>)</m:mo></m:mrow></m:math> {L}^{1}\left({\bf{R}}) ), then the damping is non-effective to the long-time behavior of the solution.
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The boundedness of Marcinkiewicz integrals commutators on non-homogeneous metric measure spaces

2015-08-26
Yonghui Cao , Jiang Zhou
Let $(\mathcal{X},d,\mu)$ be a metric measure space satisfying the upper doubling condition and geometrically doubling condition in the sense of Hytönen. In this paper, the authors establish the boundedness of … Let $(\mathcal{X},d,\mu)$ be a metric measure space satisfying the upper doubling condition and geometrically doubling condition in the sense of Hytönen. In this paper, the authors establish the boundedness of the commutator generated by the $\operatorname {RBMO}(\mu)$ function and the Marcinkiewicz integral with kernel satisfying a Hörmander-type condition, respectively, from $L^{p}(\mu)$ with $1< p<\infty$ to itself.
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Monotonicity of zeros of polynomials orthogonal with respect to an even weight function

2014-04-08
Kerstin Jordaan , H. Wang , Jiang Zhou
The monotonicity properties of all the zeros with respect to a parameter of orthogonal polynomials associated with an even weight function are studied. The results we obtain extend the work … The monotonicity properties of all the zeros with respect to a parameter of orthogonal polynomials associated with an even weight function are studied. The results we obtain extend the work of A. Markoff. The monotonicity of the zeros of Gegenbauer, Freud-type and symmetric Meixner–Pollaczek orthogonal polynomials as well as Al-Salam–Chihara q-orthogonal polynomials are investigated. For the Meixner–Pollaczek polynomials, a special case of a conjecture by Jordaan and Toókos which concerns the interlacing of their zeros between two different sequences of Meixner–Pollaczek polynomials is proved.
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On the nullity of connected graphs with least eigenvalue at least -2

2013-01-01
Jiang Zhou , Lizhu Sun , Hongmei Yao +1 more
Let L (resp. L+) be the set of connected graphs with least adjacency eigenvalue at least -2 (resp. larger than -2). The nullity of a graph G, denoted by ?(G), … Let L (resp. L+) be the set of connected graphs with least adjacency eigenvalue at least -2 (resp. larger than -2). The nullity of a graph G, denoted by ?(G), is the multiplicity of zero as an eigenvalue of the adjacency matrix of G. In this paper, we give the nullity set of L+ and an upper bound on the nullity of exceptional graphs. An expression for the nullity of generalized line graphs is given. For G ? L, if ?(G) is sufficiently large, then G is a proper generalized line graph (G is not a line graph).
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Estimates for fractional type Marcinkiewicz integrals with non-doubling measures

2014-08-18
Guanghui Lü , Jiang Zhou
Under the assumption that μ is a non-doubling measure on satisfying the growth condition, the authors prove that the fractional type Marcinkiewicz integral ℳ is bounded from the Hardy space … Under the assumption that μ is a non-doubling measure on satisfying the growth condition, the authors prove that the fractional type Marcinkiewicz integral ℳ is bounded from the Hardy space to the Lebesgue space for with kernel satisfying a certain Hörmander-type condition. In addition, the authors show that for , ℳ is bounded from the Morrey space to the space and from the Lebesgue space to the space . MSC:46A20, 42B25, 42B35.
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l k,s -Singular values and spectral radius of partially symmetric rectangular tensors

2015-09-21
Hongmei Yao , Bingsong Long , Changjiang Bu +1 more

Signless Laplacian spectral characterization of graphs with isolated vertices

2016-01-01
Shaobin Huang , Jiang Zhou , Changjiang Bu
A graph is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a DQS graph G, we show that G ? … A graph is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a DQS graph G, we show that G ? rK1 is DQS under certain conditions. Applying these results, some DQS graphs with isolated vertices are obtained.
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Singular value inclusion sets of rectangular tensors

2018-05-10
Hongmei Yao , Can Zhang , Lei Liu +2 more

New endpoint estimates for commutators of multilinear operators

2025-05-01
Yichun Zhao , Songbai Wang , Jiang Zhou

Some characterizations of BMO spaces via commutators of maximal functions on Morrey-Lorentz spaces

2025-04-11
Heng Yang , Jiang Zhou
In this paper, we investigate the commutators of the fractional maximal function and the sharp maximal function in Morrey-Lorentz spaces. Furthermore, we present some new characterizations of BMO spaces. In this paper, we investigate the commutators of the fractional maximal function and the sharp maximal function in Morrey-Lorentz spaces. Furthermore, we present some new characterizations of BMO spaces.

A composition method for neat formulas of chromatic symmetric functions

2025-04-03
David G. L. Wang , Jiang Zhou

Matrix-weighted fractional type operators on spaces of homogeneous type

2025-03-28
Yuxun Zhang , Jiang Zhou

Dynamic Analysis of a 10-Dimensional Fractional-Order Hyperchaotic System Using Advanced Hyperchaotic Metrics

2025-01-24
Muhammad Sarfraz , Jiang Zhou , Mazhar Islam +2 more
In this paper, we propose an innovative approach to fractional-order dynamics by introducing a 10-dimensional (10D) chaotic system that leverages the intrinsic memory characteristic of the Grünwald–Letnikov (G-L) derivative. We … In this paper, we propose an innovative approach to fractional-order dynamics by introducing a 10-dimensional (10D) chaotic system that leverages the intrinsic memory characteristic of the Grünwald–Letnikov (G-L) derivative. We utilize Lyapunov exponents as a quantitative measure to characterize hyperchaotic behavior, and classify the nature of the suggested 10D fractional-order system (FOS). While several methods exist for calculating Lyapunov exponents (LEs) through the utilization of integer-order systems, these approaches are not applicable for FOS due to its non-local nature. Initially, the system dynamics are thoroughly examined through Lyapunov exponents and bifurcation analysis, considering the influence of both state variables and fractional orders. To assess the hyperchaotic behavior of the proposed model, sensitivity analyses are conducted by exploring changes in state variables under two distinct initial conditions, along with time history simulations for various parameter settings. Furthermore, we examine the impact of different fractional-order sets on the system’s dynamics. A comprehensive performance comparison is conducted between the proposed 10-dimensional fractional-order hyperchaotic system and several existing hyperchaotic systems. This comparison utilizes advanced metrics, including the Kolmogorov–Sinai (KS) entropy, Kaplan–Yorke dimension, the Perron effect analysis, and the 0-1 test for chaos. Simulation outcomes reveal that the proposed system surpasses existing algorithms, delivering improved precision and accuracy.

Hyers–Ulam stability of norm-additive functional equations via $(\delta , \epsilon )$-isometries

2025-01-03
Muhammad Sarfraz , Jiang Zhou , Yongjin Li
This research examines the Hyers–Ulam stability of norm-additive functional equations expressed as $$\begin{aligned}& \|\xi (gh^{-1})\|=\|\xi (g)-\xi (h)\|,\\& \|\xi (gh)\|=\|\xi (g)+\xi (h)\|, \end{aligned}$$ through the utilization of $(\delta , \epsilon )$ … This research examines the Hyers–Ulam stability of norm-additive functional equations expressed as $$\begin{aligned}& \|\xi (gh^{-1})\|=\|\xi (g)-\xi (h)\|,\\& \|\xi (gh)\|=\|\xi (g)+\xi (h)\|, \end{aligned}$$ through the utilization of $(\delta , \epsilon )$ -isometries. In this context, $\xi : G \to X$ represents a surjective (δ-surjective) mapping, where G denotes noncommutative group (arbitrary group) and X signifies a Banach space (or a real Banach space).

Hardy–Littlewood maximal operators and generalized Orlicz spaces on measure spaces

2025-01-01
Haiyan Zhou , Xiaoqian Song , Songbai Wang +1 more

Morrey spaces on weighted homogeneous trees

2025-01-01
Xuhong Qian , Jiang Zhou

Necessary and sufficient conditions for boundedness of commutators of parametric Marcinkiewicz integrals with weighted Lipschitz functions

2024-11-29
Heng Yang , Jiang Zhou
In this paper, we obtain the sharp maximal function estimate for the commutator $\mathcal{M}_{\Omega,b}^{\rho,m}$ generated by the parametric Marcinkiewicz integral $\mathcal{M}_{\Omega}^{\rho,m}$ and the locally integrable function $b$, where $\rho&gt;0$, $m&gt;1$ … In this paper, we obtain the sharp maximal function estimate for the commutator $\mathcal{M}_{\Omega,b}^{\rho,m}$ generated by the parametric Marcinkiewicz integral $\mathcal{M}_{\Omega}^{\rho,m}$ and the locally integrable function $b$, where $\rho&gt;0$, $m&gt;1$ and $\Omega$ satisfies certain log-type regularity condition. Meanwhile, we prove the commutator $\mathcal{M}_{\Omega,b}^{\rho,m}$ is bounded from $L^p(\mu)$ to $L^q(\mu^{1-q})$ if and only if $b\in Lip_\beta(\mu)$, where $\mu\in A_1,0 \beta 1,1 p n/\beta$ and $1/q=1/p-\beta/n$.

Unified bounds for the independence number of graph powers

2024-11-14
Aida Abiad , Jiang Zhou
For a graph $G$, its $k$-th power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$ of each other. The $k$-independence number $\alpha_k(G)$ … For a graph $G$, its $k$-th power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$ of each other. The $k$-independence number $\alpha_k(G)$ is defined as the independence number of $G^k$. By using general semidefinite programming and polynomial methods, we derive sharp bounds for the $k$-independence number of a graph, which extend and unify various existing results. Our work also allows us to easily derive some new bounds for $\alpha_k(G)$.
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Stabilities of Norm-Additive Functional Equations Over Noncommutative Group Through $$(\delta , \theta , \epsilon )$$-isometry

2024-11-13
Muhammad Sarfraz , Yongjin Li , Jiang Zhou

Homogeneous Grand Mixed Herz–Morrey Spaces and Their Applications

2024-10-16
Xiaoxi Xia , Jiang Zhou
In this paper, we introduce the homogeneous grand mixed Herz–Morrey spaces MK˙q˜,λα,p),θ(Rn) and investigate their fundamental properties. We further explore the boundedness of sublinear operators and fractional-type operators on these … In this paper, we introduce the homogeneous grand mixed Herz–Morrey spaces MK˙q˜,λα,p),θ(Rn) and investigate their fundamental properties. We further explore the boundedness of sublinear operators and fractional-type operators on these spaces, establishing new results that contribute to the broader understanding of their applications.

Variable Lebesgue Space over Weighted Homogeneous Tree

2024-09-30
Yuxun Zhang , Jiang Zhou
An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T=(V,E) with the natural distance d … An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T=(V,E) with the natural distance d defined on graphs and a weighted measure μ of exponential growth, the authors introduce the variable Lebesgue space Lp(·)(μ) over (V,d,μ) and investigate it under the global Hölder continuity condition for p(·). As an application, the strong and weak boundedness of the maximal operator relevant to admissible trapezoids on Lp(·)(μ) is obtained, and an unbounded example is presented.

An 8D Hyperchaotic System of Fractional-Order Systems Using the Memory Effect of Grünwald–Letnikov Derivatives

2024-09-11
Muhammad Sarfraz , Jiang Zhou , Fateh Ali
We utilize Lyapunov exponents to quantitatively assess the hyperchaos and categorize the limit sets of complex dynamical systems. While there are numerous methods for computing Lyapunov exponents in integer-order systems, … We utilize Lyapunov exponents to quantitatively assess the hyperchaos and categorize the limit sets of complex dynamical systems. While there are numerous methods for computing Lyapunov exponents in integer-order systems, these methods are not suitable for fractional-order systems because of the nonlocal characteristics of fractional-order derivatives. This paper introduces innovative eight-dimensional chaotic systems that investigate fractional-order dynamics. These systems exploit the memory effect inherent in the Grünwald–Letnikov (G-L) derivative. This approach enhances the system’s applicability and compatibility with traditional integer-order systems. An 8D Chen’s fractional-order system is utilized to showcase the effectiveness of the presented methodology for hyperchaotic systems. The simulation results demonstrate that the proposed algorithm outperforms existing algorithms in both accuracy and precision. Moreover, the study utilizes the 0–1 Test for Chaos, Kolmogorov–Sinai (KS) entropy, the Kaplan–Yorke dimension, and the Perron Effect to analyze the proposed eight-dimensional fractional-order system. These additional metrics offer a thorough insight into the system’s chaotic behavior and stability characteristics.

Isometries to Analyze the Stability of Norm-Based Functional Equations in p-Uniformly Convex Spaces

2024-07-01
Muhammad Sarfraz , Jiang Zhou , Mazhar Islam +1 more
Over the past two decades, significant advancements have been made in understanding the stability according to Hyers–Ulam involving different functional equations (FEs). This study investigates the generalized stability of norm-based … Over the past two decades, significant advancements have been made in understanding the stability according to Hyers–Ulam involving different functional equations (FEs). This study investigates the generalized stability of norm-based (norm-additive) FEs within the framework of arbitrary (noncommutative) groups and p-uniformly convex spaces. Specifically, we analyze two key functional equations, ∥η(gh)∥=∥η(g)+η(h)∥ and ∥η(gh−1)∥=∥η(g)−η(h)∥foreveryg,h∈G, where (G,·) denotes an arbitrary group and B is considered to be a p-uniformly convex space. The surjectivity of the function η:G→B is a critical assumption in our analysis. Drawing upon the foundational works of L. Cheng and M. Sarfraz, this paper applies the large perturbation method tailored for p-uniformly convex spaces, where p≥1. This study extends previous research by offering a deeper exploration of the conditions under which these functional equations demonstrate Hyers–Ulam stability. In this study, the additive functional equation demonstrates a fundamental form of symmetry, where the order of operands does not affect the results. This symmetry under permutation of arguments is crucial for the analysis of stability. In the context of norm-additive FEs, this stability criterion investigates how small changes in the inputs of a functional equation affect the outputs, especially when the function is expected to follow an additive form.
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The high order spectral extremal results for graphs and their applications

2024-06-22
Chunmeng Liu , Jiang Zhou , Changjiang Bu

On the Generalized Stabilities of Functional Equations via Isometries

2024-06-14
Muhammad Sarfraz , Jiang Zhou , Yongjin Li +1 more
The main goal of this research article is to investigate the stability of generalized norm-additive functional equations. This study demonstrates that these equations are Hyers-Ulam stable for surjective functions from … The main goal of this research article is to investigate the stability of generalized norm-additive functional equations. This study demonstrates that these equations are Hyers-Ulam stable for surjective functions from an arbitrary group G to a real Banach space B using the large perturbation method. Furthermore, hyperstability results are investigated for a generalized Cauchy equation.
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A combinatorial problem related to the classical probability

2024-05-03
Jiang Zhou
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Weak type estimates of genuine Calderón–Zygmund operators on the local Morrey spaces associated with ball quasi-Banach function spaces

2024-03-25
Mingwei Shi , Jiang Zhou , Songbai Wang

Spherical two-distance sets and graph eigenvalues

2024-02-18
Jiang Zhou
Let $N_{\alpha,\beta}(d)$ denote the maximum size of a spherical two-distance set in $\mathbb{R}^d$ such that the inner products of distinct vectors only take $\alpha$ and $\beta$. By considering the correspondence … Let $N_{\alpha,\beta}(d)$ denote the maximum size of a spherical two-distance set in $\mathbb{R}^d$ such that the inner products of distinct vectors only take $\alpha$ and $\beta$. By considering the correspondence between spherical two-distance sets and graphs with specific spectral properties, we determine $N_{\alpha,\beta}(d)$ for fixed $-1\leq\beta<0\leq\alpha<1$ and sufficiently large $d$, which extends the work in [Equiangular lines with a fixed angle, Ann. Math. 194 (2021) 729-743] and [Spherical two-distance sets and eigenvalues of signed graphs, Combinatorica 43 (2023) 203-232]. The limit $\lim_{d\rightarrow\infty}N_{\alpha,\beta}(d)/d$ is also derived from our work, that is, the problem of determining $\lim_{d\rightarrow\infty}N_{\alpha,\beta}(d)/d$ for any fixed $-1\leq\beta<0\leq\alpha<1$ is completely solved in the spherical $\{\alpha,\beta\}$-code setting.
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Generalized Vincze’s functional equations on any group in connection with the maximum functional equation

2024-02-01
Muhammad Sarfraz , Jiang Zhou , Qi Liu +1 more

Compactness of commutators of fractional integral operators on ball Banach function spaces

2024-01-01
Heng Yang , Jiang Zhou
&lt;abstract&gt;&lt;p&gt;Let $ 0 &amp;lt; \alpha &amp;lt; n $ and $ b $ be a locally integrable function. In this paper, we obtain the characterization of compactness of the iterated commutator … &lt;abstract&gt;&lt;p&gt;Let $ 0 &amp;lt; \alpha &amp;lt; n $ and $ b $ be a locally integrable function. In this paper, we obtain the characterization of compactness of the iterated commutator $ (T_{\Omega, \alpha})_{b}^{m} $ generated by the function $ b $ and the fractional integral operator with the homogeneous kernel $ T_{\Omega, \alpha} $ on ball Banach function spaces. As applications, we derive the characterization of compactness via the commutator $ (T_{\Omega, \alpha})_b^m $ on weighted Lebesgue spaces, and further obtain a necessary and sufficient condition for the compactness of the iterated commutator $ (T_{\alpha})_{b}^{m} $ generated by the function $ b $ and the fractional integral operator $ T_\alpha $ on Morrey spaces. Moreover, we also show the necessary and sufficient condition for the compactness of the commutator $ [b, T_{\alpha}] $ generated by the function $ b $ and the fractional integral operator $ T_\alpha $ on variable Lebesgue spaces and mixed Morrey spaces.&lt;/p&gt;&lt;/abstract&gt;

Global well-posedness of the 3D generalized Boussinesq equations

2024-01-01
Bo Xu , Jiang Zhou
In this paper, we consider the 3D generalized incompressible Boussinesq equations in $ \chi^{1-2\alpha} $. However, the main difficulty lies in how to handle the terms $ (u\cdot\nabla)\theta $ and … In this paper, we consider the 3D generalized incompressible Boussinesq equations in $ \chi^{1-2\alpha} $. However, the main difficulty lies in how to handle the terms $ (u\cdot\nabla)\theta $ and $ \theta e_{3} $. This paper overcomes this challenge in two ways, making it possible to study the global well-posedness. One is to eliminate the term $ \theta e_{3} $ by adding general time-dependent viscosity coefficients, and the other is to introduce a damping term to make the thermal decay faster.
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Global regularity of the 3D generalized Navier-Stokes equations with damping term

2024-01-01
Bo Xu , Jiang Zhou
In this paper, we establish the global existence and uniqueness of strong solution to the three-dimensional generalized Navier-Stokes equations with nonlinear damping term. In this paper, we establish the global existence and uniqueness of strong solution to the three-dimensional generalized Navier-Stokes equations with nonlinear damping term.

Some estimates of multilinear operators on tent spaces

2024-01-01
Heng Yang , Jiang Zhou
&lt;p&gt;Let $ 0 &amp;lt; \alpha &amp;lt; mn $ and $ 0 &amp;lt; r, q &amp;lt; \infty $. In this paper, we obtain the boundedness of some multilinear operators by establishing … &lt;p&gt;Let $ 0 &amp;lt; \alpha &amp;lt; mn $ and $ 0 &amp;lt; r, q &amp;lt; \infty $. In this paper, we obtain the boundedness of some multilinear operators by establishing pointwise inequalities and applying extrapolation methods on tent spaces $ T_{r}^{q}(\mathbb{R}_{+}^{n+1}) $, where these multilinear operators include multilinear Hardy–Littlewood maximal operator $ \mathcal{M} $, multilinear fractional maximal operator $ \mathcal{M}_{\alpha} $, multilinear Calderón–Zygmund operator $ \mathcal{T} $, and multilinear fractional integral operator $ \mathcal{I}_{\alpha} $. Therefore, the results of Auscher and Prisuelos–Arribas [Math. Z. &lt;bold&gt;286&lt;/bold&gt; (2017), 1575–1604] are extended to the general case.&lt;/p&gt;

New mixed Herz-Hardy spaces and their applications

2024-01-01
Yichun Zhao , Mingquan Wei , Jiang Zhou
In this paper, Herz-Hardy spaces with mixed-norm are introduced, and some properties of these spaces are established, such as the characterization of various maximal operators, including property and some inequalities. … In this paper, Herz-Hardy spaces with mixed-norm are introduced, and some properties of these spaces are established, such as the characterization of various maximal operators, including property and some inequalities. Furthermore, we investigate atomic decomposition and molecular decomposition of mixed-norm Herz-Hardy spaces. As an application, the authors obtain the boundedness of some operators on these spaces by atomic decomposition.

Unified bounds for the independence number of graphs

2023-12-11
Jiang Zhou
Abstract The Hoffman ratio bound, Lovász theta function, and Schrijver theta function are classical upper bounds for the independence number of graphs, which are useful in graph theory, extremal combinatorics, … Abstract The Hoffman ratio bound, Lovász theta function, and Schrijver theta function are classical upper bounds for the independence number of graphs, which are useful in graph theory, extremal combinatorics, and information theory. By using generalized inverses and eigenvalues of graph matrices, we give bounds for independence sets and the independence number of graphs. Our bounds unify the Lovász theta function, Schrijver theta function, and Hoffman-type bounds, and we obtain the necessary and sufficient conditions of graphs attaining these bounds. Our work leads to some simple structural and spectral conditions for determining a maximum independent set, the independence number, the Shannon capacity, and the Lovász theta function of a graph.
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Some characterizations of Lipschitz spaces via commutators of the Hardy-Littlewood maximal operator on slice spaces

2023-09-30
Heng Yang , Jiang Zhou
Let M be the Hardy-Littlewood maximal operator and b be a locally integrable function. Denote by M_b and [b,M] the maximal commutator and the nonlinear commutator of M with b. … Let M be the Hardy-Littlewood maximal operator and b be a locally integrable function. Denote by M_b and [b,M] the maximal commutator and the nonlinear commutator of M with b. In this paper, we give necessary and sufficient conditions for the boundedness of M_b and [b,M] on slice spaces when the function b belongs to Lipschitz spaces, by which a new characterization of non-negative Lipschitz functions is obtained.

Necessary and Sufficient Conditions for Commutator of the Calderón–Zygmund Operator on Mixed-Norm Herz-Slice Spaces

2023-09-13
Lihua Zhang , Jiang Zhou
We obtain the separability of mixed-norm Herz-slice spaces, establish a weak convergence on mixed-norm Herz-slice spaces, and get the boundedness of the Calderón–Zygmund operator T on mixed-norm Herz-slice spaces. Moreover, … We obtain the separability of mixed-norm Herz-slice spaces, establish a weak convergence on mixed-norm Herz-slice spaces, and get the boundedness of the Calderón–Zygmund operator T on mixed-norm Herz-slice spaces. Moreover, we get the necessary and sufficient conditions for the boundedness of the commutator [b,T] on mixed-norm Herz-slice spaces, where b is a locally integrable function.
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Operators on Mixed-Norm Amalgam Spaces via Extrapolation

2023-08-01
Y. Lu , Jiang Zhou , Shanwen Wang

Oriented spanning trees and stationary distribution of digraphs

2023-07-03
Jiang Zhou , Changjiang Bu
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Weighted Norm Inequalities for Calderón–Zygmund Operators of $$\phi$$-Type and Their Commutators

2023-06-28
Hang Li , Jiang Zhou

Boundedness for Littlewood-Paley functions on weighted Morrey-type spaces related to certain nonnegative potentials

2023-06-19
N. Zhao , Jiang Zhou , Yu Liu

Characterizations of the BMO and Lipschitz Spaces via Commutators on Weak Lebesgue and Morrey Spaces

2023-06-17
Dinghuai Wang , Jiang Zhou
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Some estimates of operators on Local mixed Morrey-type spaces

2023-05-25
Mingwei Shi , Jiang Zhou

Some estimates of multi-sublinear operators and commutators on mixed $$\lambda $$-central Morrey spaces

2023-02-24
Wenna Lu , Jiang Zhou

Boundedness of intrinsic square functions and commutators on generalized central Morrey spaces

2023-01-17
Wenna Lu , Jiang Zhou
In this paper, the authors establish the boundedness for a large class of intrinsic square functions Gα, gα, gλ~,α∗ and their commutators [b,Gα], [b,gα] and [b,gλ~,α∗] generated with λ-central BMO … In this paper, the authors establish the boundedness for a large class of intrinsic square functions Gα, gα, gλ~,α∗ and their commutators [b,Gα], [b,gα] and [b,gλ~,α∗] generated with λ-central BMO functions b∈CBMOp,λ(Rn) on generalized central Morrey spaces Bq,φ(Rn) for 1<q<∞,0<α≤1, respectively. All of the results are new even on the central Morrey spaces Bq,λ(Rn).
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Blow-up for compressible Euler system with space-dependent damping in 1-D

2023-01-01
Jinbo Geng , N. Lai , Manwai Yuen +1 more
Abstract This article considers the Cauchy problem for compressible Euler system in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="bold">R</m:mi></m:math> {\bf{R}} with damping, in which the coefficient depends on the space variable. Assuming the initial … Abstract This article considers the Cauchy problem for compressible Euler system in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="bold">R</m:mi></m:math> {\bf{R}} with damping, in which the coefficient depends on the space variable. Assuming the initial density has a small perturbation around a constant state and both the small perturbation and the small initial velocity field are compact supported, finite-time blow-up result will be established. This result reveals the fact that if the space-dependent damping coefficient decays fast enough in the far field (belongs to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mrow><m:mi>L</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msup><m:mrow><m:mo>(</m:mo><m:mrow><m:mi mathvariant="bold">R</m:mi></m:mrow><m:mo>)</m:mo></m:mrow></m:math> {L}^{1}\left({\bf{R}}) ), then the damping is non-effective to the long-time behavior of the solution.
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Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications

2023-01-01
Yichun Zhao , Jiang Zhou
Abstract In this article, we introduce anisotropic mixed-norm Herz spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mo>˙</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>q</m:mi> </m:mrow> … Abstract In this article, we introduce anisotropic mixed-norm Herz spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mo>˙</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent="true"> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent="true"> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and investigate some basic properties of those spaces. Furthermore, we establish the Rubio de Francia extrapolation theory, which resolves the boundedness problems of Calderón-Zygmund operators and fractional integral operator and their commutators, on spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mo>˙</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent="true"> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent="true"> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) . Especially, the Littlewood-Paley characterizations of anisotropic mixed-norm Herz spaces are also gained. As the generalization of anisotropic mixed-norm Herz spaces, we introduce anisotropic mixed-norm Herz-Hardy spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>H</m:mi> <m:msubsup> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mo>˙</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent="true"> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> H{\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>H</m:mi> <m:msubsup> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> <m:mo>,</m:mo> <m:mover accent="true"> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mo>→</m:mo> </m:mrow> </m:mover> </m:mrow> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> </m:mrow> </m:msubsup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> H{K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) , on which atomic decomposition and molecular decomposition are obtained. Moreover, we gain the boundedness of classical Calderón-Zygmund operators.
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CBMO estimates for some multilinear operators on mixed Herz spaces

2023-01-01
Yi Zhao , Mingq an Wei , Jiang Zhou
In this paper, we develop the CBMO estimates for the multilinear operators of singular integral operator, fractional integral operator, and Hardy-type operators in higher dimensional cases, which include their commutators … In this paper, we develop the CBMO estimates for the multilinear operators of singular integral operator, fractional integral operator, and Hardy-type operators in higher dimensional cases, which include their commutators as special cases, on mixed Herz spaces.Furthermore, some endpoint cases are also obtained, such as Hardy-type and weak-type estimates for multilinear operators.Particularly, it is demonstrated that in some extreme cases, these operators are actually not bounded.
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Some estimates of multilinear operators on weighted amalgam spaces $$(L^p,L^q_w)_t(\mathbb R^n)$$

2022-10-01
Y. Lu , S. B. Wang , Jiang Zhou

Necessary and sufficient conditions for boundedness of commutators associated with Calderón–Zygmund operators on slice spaces

2022-08-08
Yuan Lu , Jiang Zhou , Songbai Wang

The high order spectrum of a graph and its applications in graph colouring and clique counting

2022-07-31
Chunmeng Liu , Jiang Zhou , Changjiang Bu
D. Cvetković, M. Doob and H. Sachs considered the high order eigenvalue problems of graphs. The high order eigenvalues of a graph G are solutions of the high degree homogeneous … D. Cvetković, M. Doob and H. Sachs considered the high order eigenvalue problems of graphs. The high order eigenvalues of a graph G are solutions of the high degree homogeneous polynomial equations derived from G. We propose the adjacency tensor A(G) of a graph G and show that the high order eigenvalues of G can be regarded as eigenvalues of A(G). Some results of the spectrum of the adjacency matrix are extended to the spectrum of A(G) by using the spectral theory of nonnegative tensors. An upper bound of chromatic number is given via the spectral radius of A(G). Our upper bound is a generalization of Wilf's bound χ(G)≤ρ(G)+1 (where ρ(G) is the spectral radius of the adjacency matrix of a graph G) and sharper than the bound of Wilf in some classes of graphs. A formula of the number of cliques of fixed size which involve the spectrum of A(G) is obtained.

The boundedness of fractional integral operators in local and global mixed Morrey-type spaces

2022-02-01
Houkun Zhang , Jiang Zhou
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Mixed-Norm Amalgam Spaces and Their Predual

2022-01-04
Houkun Zhang , Jiang Zhou
In this paper, we introduce mixed-norm amalgam spaces (Lp→,Ls→)α(Rn) and prove the boundedness of maximal function. Then, the dilation argument obtains the necessary and sufficient conditions of fractional integral operators’ … In this paper, we introduce mixed-norm amalgam spaces (Lp→,Ls→)α(Rn) and prove the boundedness of maximal function. Then, the dilation argument obtains the necessary and sufficient conditions of fractional integral operators’ boundedness. Furthermore, the strong estimates of linear commutators [b,Iγ] generated by b∈BMO(Rn) and Iγ on mixed-norm amalgam spaces (Lp→,Ls→)α(Rn) are established as well. In order to obtain the necessary conditions of fractional integral commutators’ boundedness, we introduce mixed-norm Wiener amalgam spaces (Lp→,Ls→)(Rn). We obtain the necessary and sufficient conditions of fractional integral commutators’ boundedness by the duality theory. The necessary conditions of fractional integral commutators’ boundedness are a new result even for the classical amalgam spaces. By the equivalent norm and the operators Str(p)(f)(x), we study the duality theory of mixed-norm amalgam spaces, which makes our proof easier. In particular, note that predual of the primal space is not obtained and the predual of the equivalent space does not mean the predual of the primal space.
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A Characterization of Weighted Central Campanato Spaces

2021-11-01
Teng Ma , Jiang Zhou

Two-weight norm inequalities for some fractional type operators related to Schrödinger operator on weighted Morrey spaces

2021-10-12
W.X. Wu , Jiang Zhou
In this paper, we establish the two-weight norm inequalities for fractional maximal functions and fractional integral operators related to Schrödinger differential operator on weighted Morrey spaces related to certain nonnegative … In this paper, we establish the two-weight norm inequalities for fractional maximal functions and fractional integral operators related to Schrödinger differential operator on weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.
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Erratum to: The boundedness of commutators of sublinear operators on Herz Triebel-Lizorkin spaces

2021-09-07
Chenglong Fang , Jiang Zhou
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Spectral radius and clique partitions of graphs

2021-08-05
Jiang Zhou , Edwin van Dam
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Characterizations of Weighted BMO Space and Its Application

2021-08-01
Ding Huai Wang , Jiang Zhou , Zhi Dong Teng
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Coauthor Papers Together
Changjiang Bu 52
Dinghuai Wang 20
Zhidong Teng 12
Lizhu Sun 10
Lizhu Sun 9
Yimin Wei 8
Wenzhe Wang 7
Muhammad Sarfraz 7
Yonghui Cao 6
Songbai Wang 5
Heng Yang 4
Yongjin Li 4
Wenzhe Wang 4
Yichun Zhao 4
N. Zhao 4
Wenyi Chen 3
Hongmei Yao 3
Bolin Ma 3
Haifeng Li 3
Guanghui Lü 3
Chenglong Fang 3
Hongbo Li 2
Xi Hu 2
Xiuqing Zhou 2
Mingwei Shi 2
Y. Lu 2
Tianyi Bu 2
Lijun Yu 2
Chunmeng Liu 2
Teng Ma 2
Yuxun Zhang 2
Bo Xu 2
Wenna Lu 2
Ronghui Liu 2
Houkun Zhang 2
Mazhar Islam 2
Suixin He 2
Houkun Zhang 2
Xu Zhang 2
Yuanpeng Wei 2
Yuan Lu 2
Haiyan Zhou 1
David G. L. Wang 1
Heng Yang 1
Xiaoqian Song 1
S. B. Wang 1
Cao Yonghui 1
N. Lai 1
Jihong Shen 1
Kerstin Jordaan 1

Eigenvalues of a real supersymmetric tensor

2005-06-20
Liqun Qi
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Factorization Theorems for Hardy Spaces in Several Variables

1976-05-01
Ronald R. Coifman , Richard Rochberg , Guido Weiss
The purpose of this paper is to extend to Hardy spaces in several variables certain well known factorization theorems on the unit disk. The extensions will be carried out for … The purpose of this paper is to extend to Hardy spaces in several variables certain well known factorization theorems on the unit disk. The extensions will be carried out for various spaces of holomorphic functions on the unit ball of C as well as for Hardy spaces defined by the Riesz systems on R. These results together with their proofs yield new characterizations of the space BMO (Bounded Mean Oscillation) and show a close relationship between BMO functions and certain linear operators on various LI and H2 spaces. The main tools are the result of Fefferman and Stein [8] on the duality between HI and BMO and a new characterization of BMO in terms of boundedness on L2 of the commutator of a singular integral operator with a multiplication operator. We begin by illustrating these ideas in the one dimensional case: Let F be holomorphic in {I z I < 1} and satisfy sup, 5 F(rete) I dO ? 1 (i.e., F is in H'(dO)). It is well known that F = GG2 with G1, G2 holomorphic and sup, I G,(rel0) 1' ! 1 (i.e., G, e H2(dO)). Write F = f + if, G, = gj + ig withf, g1, g, real. Thenf = Im(GG2) = sg1 1 + gi. Thusafunction f is an imaginary (or real) part of an HI function if and only if it can be represented as glg2 + g192 for L2 functions g, and g2. Furthermore,

An introduction to the theory of graph spectra

2010-10-01
Dragoš Cvetković , Peter Rowlinson , Slobodan Simić
This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined … This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.

Singular Values and Eigenvalues of Tensors: A Variational Approach

2006-01-18
Lek‐Heng Lim
We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These … We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are particularly useful in generalizing certain areas where the spectral theory of matrices has traditionally played an important role. For illustration, we will discuss a multilinear generalization of the Perron-Frobenius theorem.
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New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory

2008-12-14
Andrei K. Lerner , Sheldy Ombrosi , Carlos Pérez +2 more
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Multilinear Calderón–Zygmund Theory

2002-01-01
Loukas Grafakos , Rodolfo H. Torres

Mean oscillation and commutators of singular integral operators

1978-12-01
Svante Janson
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On the compactness of operators of Hankel type

1978-01-01
Akihito Uchiyama
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Multilinear estimates and fractional integration

1999-01-01
Carlos E. Kenig , Elias M. Stein
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On the solutions of quasi-linear elliptic partial differential equations

1938-01-01
Charles B. Morrey
In this paper, we are concerned with the existence and differentiability properties of the solutions of "quasi-linear" elliptic partial differential equations in two variables, i.e In this paper, we are concerned with the existence and differentiability properties of the solutions of "quasi-linear" elliptic partial differential equations in two variables, i.e
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Some Spectral Properties of Uniform Hypergraphs

2014-10-30
Jiang Zhou , Lizhu Sun , Wenzhe Wang +1 more
For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the Laplacian tensor of $H$, which imply that $\sum_{i=1}^nd_i^s$ ($s=1,\ldots,k$) is determined by the Laplacian spectrum of $H$, where … For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the Laplacian tensor of $H$, which imply that $\sum_{i=1}^nd_i^s$ ($s=1,\ldots,k$) is determined by the Laplacian spectrum of $H$, where $d_1,\ldots,d_n$ is the degree sequence of $H$. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spectral characterizations of odd-bipartite hypergraphs, and give a partial answer to a question posed by Shao et al (2014). We also give some spectral properties of power hypergraphs, and show that a conjecture posed by Hu et al (2013) holds under certain conditons.
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Sharp maximal function estimates for multilinear singular integrals

2003-01-01
Carlos Pérez , Rodolfo H. Torres
A new proof of a weighted norm inequality for multilinear singu- lar integrals of Calderon-Zygmund type is presented through a more general estimate involving a sharp maximal function. An application … A new proof of a weighted norm inequality for multilinear singu- lar integrals of Calderon-Zygmund type is presented through a more general estimate involving a sharp maximal function. An application is given to the study of certain multilinear commutators. The study of multilinear singular integrals of Calderon-Zygmun type continues to attract many researchers. Many results obtained parallel the linear theory of classical Calderon-Zygmund operators but new interesting phenomena have also been observed. A systematic analysis of many basic properties of such operators can be found in the article by Grafakos and Torres (GT1). See also the work of Kenig and Stein (KS) and the survey article (GT2) for further references and details. One aspect of the theory that still is being developed is the one related to the study of maximal operators associated to multilinear singular integrals and appro- priate versions of multilinear weighted norm inequalities. In a recent work Grafakos and Torres (GT3) have obtained multilinear weighted norm inequalities based on a version of Cotlar's inequality in the multilinear setting. Their approach provides multilinear analogous of the works by Coifman (C) and Coifman and Feerman (CF). Here we present a dierent approach based on the use of a modified version of the sharp maximal function of Feerman

Weighted Morrey spaces and a singular integral operator

2009-01-20
Yoshio Komori , Satoru Shirai
Abstract In this paper, we shall introduce a weighted Morrey space and study the several properties of classical operatorsin harmonic analysis on this space (© 2009 WILEY‐VCH Verlag GmbH &amp; … Abstract In this paper, we shall introduce a weighted Morrey space and study the several properties of classical operatorsin harmonic analysis on this space (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

On commutators of singular integrals and bilinear singular integrals

1975-01-01
Ronald R. Coifman , Yves Meyer
${L^p}$ estimates for multilinear singular integrals generalizing Calderón’s commutator integral are obtained. The methods introduced involve Fourier and Mellin analysis. ${L^p}$ estimates for multilinear singular integrals generalizing Calderón’s commutator integral are obtained. The methods introduced involve Fourier and Mellin analysis.
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Weighted Norm Inequalities and Related Topics

1985-01-01
José Garcı́a-Cuerva , J.-L. Rubio de Francia

H&lt;sup&gt;+&lt;/sup&gt;-eigenvalues of Laplacian and signless Laplacian tensors

2014-01-01
Liqun Qi
We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph.We study their H + -eigenvalues, i.e., H-eigenvalues with nonnegative H-eigenvectors, and … We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph.We study their H + -eigenvalues, i.e., H-eigenvalues with nonnegative H-eigenvectors, and H ++ -eigenvalues, i.e., H-eigenvalues with positive H-eigenvectors.We show that each of the Laplacian tensor, the signless Laplacian tensor, and the adjacency tensor has at most one H ++ -eigenvalue, but has several other H + -eigenvalues.We identify their largest and smallest H + -eigenvalues, and establish some maximum and minimum properties of these H + -eigenvalues.We then define analytic connectivity of a uniform hypergraph and discuss its application in edge connectivity.
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Which graphs are determined by their spectrum?

2003-05-27
Edwin van Dam , Willem H. Haemers
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The space LP, with mixed norm

1961-09-01
A. Benedek , R. Panzone

On functions of bounded mean oscillation

1961-08-01
Franklin John , Louis Nirenberg

The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph

2014-01-21
Shenglong Hu , Liqun Qi
In this paper, we show that the eigenvectors of the zero Laplacian and signless Lapacian eigenvalues of a $k$-uniform hypergraph are closely related to some configured components of that hypergraph. … In this paper, we show that the eigenvectors of the zero Laplacian and signless Lapacian eigenvalues of a $k$-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector of the zero Laplacian or signless Lapacian eigenvalue have the same modulus. Moreover, under a {\em canonical} regularization, the phases of the components of these eigenvectors only can take some uniformly distributed values in $\{\{exp}(\frac{2j\pi}{k})\;|\;j\in [k]\}$. These eigenvectors are divided into H-eigenvectors and N-eigenvectors. Eigenvectors with minimal support is called {\em minimal}. The minimal canonical H-eigenvectors characterize the even (odd)-bipartite connected components of the hypergraph and vice versa, and the minimal canonical N-eigenvectors characterize some multi-partite connected components of the hypergraph and vice versa.
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A general product of tensors with applications

2013-07-30
Jia‐Yu Shao
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Weighted norm inequalities for the Hardy maximal function

1972-01-01
Benjamin Muckenhoupt
The principal problem considered is the determination of all nonnegative functions, $U(x)$, for which there is a constant, C, such that \[ \int _J {{{[{f^ \ast }(x)]}^p}U(x)dx \leqq C\int _J … The principal problem considered is the determination of all nonnegative functions, $U(x)$, for which there is a constant, C, such that \[ \int _J {{{[{f^ \ast }(x)]}^p}U(x)dx \leqq C\int _J {|f(x){|^p}U(x)dx,} } \] where $1 < p < \infty$, J is a fixed interval, C is independent of f, and ${f^ \ast }$ is the Hardy maximal function, \[ {f^ \ast }(x) = \sup \limits _{y \ne x;y \in J} \frac {1}{{y - x}}\int _x^y {|f(t)|dt.} \] The main result is that $U(x)$ is such a function if and only if \[ \left [ {\int _I {U(x)dx} } \right ]{\left [ {\int _I {{{[U(x)]}^{ - 1/(p - 1)}}dx} } \right ]^{p - 1}} \leqq K|I{|^p}\] where I is any subinterval of J, $|I|$ denotes the length of I and K is a constant independent of I. Various related problems are also considered. These include weak type results, the problem when there are different weight functions on the two sides of the inequality, the case when $p = 1$ or $p = \infty$, a weighted definition of the maximal function, and the result in higher dimensions. Applications of the results to mean summability of Fourier and Gegenbauer series are also given.
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Spectra of uniform hypergraphs

2011-12-09
Joshua Cooper , Aaron Dutle
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Endpoint Estimates for Commutators of Singular Integral Operators

1995-02-01
Carlos Pérez
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Compactness of Commutators for Singular Integrals on Morrey Spaces

2011-07-15
Yanping Chen , Yong Ding , Xinxia Wang
Abstract In this paper we characterize the compactness of the commutator [ b , T ] for the singular integral operator on the Morrey spaces . More precisely, we prove … Abstract In this paper we characterize the compactness of the commutator [ b , T ] for the singular integral operator on the Morrey spaces . More precisely, we prove that if , the -closure of , then [ b , T ] is a compact operator on the Morrey spaces for ∞ &lt; p &lt; ∞ and 0 &lt; ⋋ &lt; n . Conversely, if and [ b , T ] is a compact operator on the for some p (1 &lt; p &lt; ∞), then . Moreover, the boundedness of a rough singular integral operator T and its commutator [ b , T ] on are also given. We obtain a sufficient condition for a subset in Morrey space to be a strongly pre-compact set, which has interest in its own right.
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Weighted inequalities for multilinear fractional integral operators

2009-06-01
Kabe Moen
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On multilinear fractional integrals

1992-01-01
Loukas Grafakos
In $ℝ^n$, we prove $L^{p₁} ×...× L^{p_{K}}$ boundedness for the multilinear fractional integrals $I_α(f₁,...,f_K)(x) = ʃ f₁(x-θ₁ y)...f_K(x-θ_K y)|y|^{α-n} dy$ where the $θ_j$'s are nonzero and distinct. We also prove … In $ℝ^n$, we prove $L^{p₁} ×...× L^{p_{K}}$ boundedness for the multilinear fractional integrals $I_α(f₁,...,f_K)(x) = ʃ f₁(x-θ₁ y)...f_K(x-θ_K y)|y|^{α-n} dy$ where the $θ_j$'s are nonzero and distinct. We also prove multilinear versions of two inequalit
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Mixed Morrey spaces

2019-01-28
Toru Nogayama

Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss

1995-01-01
Maciej Paluszyński
where T is the Calderón-Zygmund singular integral operator.It is a well known result of Coifman, Rochberg and Weiss that the boundedness of this operator on L p (R n ) … where T is the Calderón-Zygmund singular integral operator.It is a well known result of Coifman, Rochberg and Weiss that the boundedness of this operator on L p (R n ) is equivalent to f being in the space BMO.In this paper we introduce a version of this operator which allows f to be in the Besov-Lipschitz class Λβ , with 0 < β < n.
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Weighted estimates for Beltrami equations

2013-02-01
Albert Clop , Victor Cruz
We obtain a priori estimates in L p (ω) for the generalized Beltrami equation, provided that the coefficients are compactly supported V M O functions with the expected ellipticity condition, … We obtain a priori estimates in L p (ω) for the generalized Beltrami equation, provided that the coefficients are compactly supported V M O functions with the expected ellipticity condition, and the weight ω lies in the Muckenhoupt class A p .As an application, we obtain improved regularity for the jacobian of certain quasiconformal mappings.
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On Spectral Hypergraph Theory of the Adjacency Tensor

2013-07-29
K. PEARSON , Tan Zhang
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Boundedness and Compactness of Integral Operators on Spaces of Homogeneous Type and Applications, II

2001-06-01
Steven G. Krantz , Song-Ying Li

$BMO, H^1$, and Calderón-Zygmund operators for non doubling measures

2001-01-01
Xavier Tolsa
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The Kolmogorov–Riesz compactness theorem

2010-01-01
Harald Hanche-Olsen , Helge Holden
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Starlike trees whose maximum degree exceed 4 are determined by their Q-spectra

2011-07-24
Changjiang Bu , Jiang Zhou

Some new trace formulas of tensors with applications in spectral hypergraph theory

2014-07-02
Jia‐Yu Shao , Liqun Qi , Shenglong Hu
We give some graph theoretical formulas for the trace of a tensor which do not involve the differential operators and auxiliary matrix. As applications of these trace formulas in the … We give some graph theoretical formulas for the trace of a tensor which do not involve the differential operators and auxiliary matrix. As applications of these trace formulas in the study of the spectra of uniform hypergraphs, we give a characterization (in terms of the traces of the adjacency tensors) of the -uniform hypergraphs whose spectra are -symmetric, thus give an answer to a question raised in Cooper and Dutle [Linear Algebra Appl. 2012;436:3268–3292]. We generalize the results in Cooper and Dutle [Linear Algebra Appl. 2012;436:3268–3292, Theorem 4.2] and Hu and Qi [Discrete Appl. Math. 2014;169:140–151, Proposition 3.1] about the -symmetry of the spectrum of a -uniform hypergraph, and answer a question in Hu and Qi [Discrete Appl. Math. 2014;169:140–151] about the relation between the Laplacian and signless Laplacian spectra of a -uniform hypergraph when is odd. We also give a simplified proof of an expression for and discuss the expression for .
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Weighted norm inequalities for fractional integrals

1974-01-01
Benjamin Muckenhoupt , Richard L. Wheeden
The principal problem considered is the determination of all nonnegative functions, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V left-parenthesis x right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation … The principal problem considered is the determination of all nonnegative functions, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V left-parenthesis x right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">V(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, such that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar upper T Subscript gamma Baseline f left-parenthesis x right-parenthesis upper V left-parenthesis x right-parenthesis double-vertical-bar Subscript q Baseline less-than-or-equal-to upper C double-vertical-bar f left-parenthesis x right-parenthesis upper V left-parenthesis x right-parenthesis double-vertical-bar Subscript p"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow> <mml:mo symmetric="true">‖</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>γ<!-- γ --></mml:mi> </mml:msub> </mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi>V</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo symmetric="true">‖</mml:mo> </mml:mrow> <mml:mi>q</mml:mi> </mml:msub> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>C</mml:mi> <mml:msub> <mml:mrow> <mml:mo symmetric="true">‖</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi>V</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo symmetric="true">‖</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">\left \|{T_\gamma }f(x)V(x)\right \|_q \leq C\left \|f(x)V(x)\right \|_p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> where the functions are defined on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R Superscript n Baseline comma 0 greater-than gamma greater-than n comma 1 greater-than p greater-than n slash gamma comma 1 slash q equals 1 slash p minus gamma slash n"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>&gt;</mml:mo> <mml:mi>γ<!-- γ --></mml:mi> <mml:mo>&gt;</mml:mo> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>&gt;</mml:mo> <mml:mi>p</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mi>n</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>γ<!-- γ --></mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>γ<!-- γ --></mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{R^n},0 &gt; \gamma &gt; n,1 &gt; p &gt; n/\gamma ,1/q = 1/p - \gamma /n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <italic>C</italic> is a constant independent of <italic>f</italic> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T Subscript gamma Baseline f left-parenthesis x right-parenthesis equals integral f left-parenthesis x minus y right-parenthesis StartAbsoluteValue y EndAbsoluteValue Superscript gamma minus n Baseline d y"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>γ<!-- γ --></mml:mi> </mml:msub> </mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mo largeop="false">∫<!-- ∫ --></mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>y</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>y</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>γ<!-- γ --></mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:mi>d</mml:mi> <mml:mi>y</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{T_\gamma }f(x) = \smallint f(x - y)|y{|^{\gamma - n}}dy</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The main result is that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V left-parenthesis x right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">V(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is such a function if and only if <disp-formula content-type="math/mathml"> \[ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis StartFraction 1 Over StartAbsoluteValue upper Q EndAbsoluteValue EndFraction integral Underscript upper Q Endscripts left-bracket upper V left-parenthesis x right-parenthesis right-bracket Superscript q Baseline d x right-parenthesis Superscript 1 slash q Baseline left-parenthesis StartFraction 1 Over StartAbsoluteValue upper Q EndAbsoluteValue EndFraction integral Underscript upper Q Endscripts left-bracket upper V left-parenthesis x right-parenthesis right-bracket Superscript minus p prime Baseline d x right-parenthesis Superscript 1 slash p prime Baseline less-than-or-equal-to upper K"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>Q</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:mrow> </mml:mfrac> <mml:msub> <mml:mo>∫<!-- ∫ --></mml:mo> <mml:mi>Q</mml:mi> </mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">[</mml:mo> <mml:mi>V</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> <mml:mi>q</mml:mi> </mml:msup> </mml:mrow> <mml:mi>d</mml:mi> <mml:mi>x</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>Q</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:mrow> </mml:mfrac> <mml:msub> <mml:mo>∫<!-- ∫ --></mml:mo> <mml:mi>Q</mml:mi> </mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">[</mml:mo> <mml:mi>V</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−<!-- − --></mml:mo> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:msup> </mml:mrow> <mml:mi>d</mml:mi> <mml:mi>x</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>K</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{\left ( {\frac {1}{{|Q|}}\int _Q {{{[V(x)]}^q}dx} } \right )^{1/q}}{\left ( {\frac {1}{{|Q|}}\int _Q {{{[V(x)]}^{ - p’}}dx} } \right )^{1/p’}} \leq K</mml:annotation> </mml:semantics> </mml:math> \] </disp-formula> where <italic>Q</italic> is any <italic>n</italic> dimensional cube, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper Q EndAbsoluteValue"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>Q</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">|Q|</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denotes the measure of <italic>Q</italic>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p prime equals p slash left-parenthesis p minus 1 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">p’ = p/(p - 1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <italic>K</italic> is a constant independent of <italic>Q</italic>. Substitute results for the cases <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p equals 1"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">p = 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q equals normal infinity"> <mml:semantics> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">q = \infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and a weighted version of the Sobolev imbedding theorem are also proved.
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Group inverse for block matrices and some related sign analysis

2011-11-25
Jiang Zhou , Changjiang Bu , Yimin Wei
The sign pattern of a real matrix M is the (0, 1, −1)-matrix obtained from M by replacing each entry by its sign. Let N ∈ ℝ n×n be a … The sign pattern of a real matrix M is the (0, 1, −1)-matrix obtained from M by replacing each entry by its sign. Let N ∈ ℝ n×n be a group invertible matrix. Let Q(N) be the set of real matrices with the same sign pattern as N. For any , if is group invertible and the group inverses of N and have the same sign pattern, then N is called an S2GI matrix. In this article, we present the existence and the representations for the group inverse of some block matrices with one or two full rank sub-blocks, and give a family of block matrices which are S2GI matrices. Applying these results, we can partially determine the sign pattern of the solution of singular linear system with index one.

Characterization of Compactness of the Commutators of Bilinear Fractional Integral Operators

2015-04-28
Lucas Chaffee , Rodolfo H. Torres
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Tent space boundedness via extrapolation

2016-11-15
Pascal Auscher , Cruz Prisuelos-Arribas
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On determinants and eigenvalue theory of tensors

2012-10-29
Shenglong Hu , Zheng‐Hai Huang , Chen Ling +1 more
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Compactness of Commutators of Riesz Potential on Morrey Spaces

2009-01-13
Yanping Chen , Yong Ding , Xinxia Wang

Hp spaces of several variables

1972-01-01
Charles Fefferman , E. M. Stein
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Anisotropic Mixed-Norm Hardy Spaces

2017-02-27
Galatia Cleanthous , Athanasios G. Georgiadis , Morten Nielsen

Further Results for Perron–Frobenius Theorem for Nonnegative Tensors

2010-01-01
Yuning Yang , Qingzhi Yang
We give further results on the Perron–Frobenius theorem for tensors, generalize other theorems from matrices to tensors, and give an equivalent condition for nonnegative irreducible tensors.MSC codes74B9915A1815A69Keywordsnonnegative tensorPerron–Frobenius theoremKy Fan … We give further results on the Perron–Frobenius theorem for tensors, generalize other theorems from matrices to tensors, and give an equivalent condition for nonnegative irreducible tensors.MSC codes74B9915A1815A69Keywordsnonnegative tensorPerron–Frobenius theoremKy Fan theoremmaxmin problem

On the representation of functions by trigonometrical integrals

1926-12-01
Norbert Wiener

Some spectral properties and characterizations of connected odd-bipartite uniform hypergraphs

2015-02-19
Jia‐Yu Shao , Haiying Shan , Baofeng Wu
A -uniform hypergraph is called odd-bipartite, if is even and there exists some proper subset of such that each edge of contains odd number of vertices in . Odd-bipartite hypergraphs … A -uniform hypergraph is called odd-bipartite, if is even and there exists some proper subset of such that each edge of contains odd number of vertices in . Odd-bipartite hypergraphs are generalizations of the ordinary bipartite graphs. We study the spectral properties of the connected odd-bipartite hypergraphs. We prove that the Laplacian H-spectrum and signless Laplacian H-spectrum of a connected -uniform hypergraph are equal if and only if is even and is odd-bipartite. We further give several spectral characterizations of the connected odd-bipartite hypergraphs. We also give a characterization for a connected -uniform hypergraph whose Laplacian spectral radius and signless Laplacian spectral radius are equal; thus, provide an answer to a question raised by L. Qi. By showing that the Cartesian product of two odd-bipartite -uniform hypergraphs is still odd-bipartite, we determine that the Laplacian spectral radius of is the sum of the Laplacian spectral radii of and , when and are both connected odd-bipartite.
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Littlewood–Paley Theory and the T(1) Theorem with Non-doubling Measures

2001-12-01
Xavier Tolsa
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Maximal operator and weighted norm inequalities for multilinear singular integrals

2002-01-01
Loukas Grafakos , Rodolfo H. Torres
The maximal operator associated with multilinear Calderon-Zygmund singular integrals is introduced and shown to be bounded on product of Lebesgue spaces. Moreover weighted norm inequalities are obtained for this maximal … The maximal operator associated with multilinear Calderon-Zygmund singular integrals is introduced and shown to be bounded on product of Lebesgue spaces. Moreover weighted norm inequalities are obtained for this maximal operator as well as for the corresponding singular integrals.

Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms

2007-05-23
Н. В. Крылов