Yu Liu

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All published works

Action	Title	Year	Authors
+ PDF Chat	BOUNDEDNESS OF DIFFERENTIAL TRANSFORMS FOR FRACTIONAL HEAT SEMIGROUPS GENERATED BY SCHRÖDINGER OPERATORS	2024	Pengtao Li Yu Liu Zhiyong Wang
+	Besov Space via Heat Semigroup on Carnot Group and Its Capacity	2024	Nan Zhao Yu Liu
+ PDF Chat	Molecular decompositions of homogeneous Besov type spaces for Laguerre function expansions and applications	2024	He Wang Nan Zhao Haihui Wang Yu Liu
+	Geometric topics related to Besov type spaces on the Grushin setting	2024	N. Zhao Zhiyong Wang Pengtao Li Yu Liu
+	BV capacity and perimeter in abstract Wiener spaces and applications	2023	Guiyang Liu He Wang Yu Liu
+	Subgraphs of $$\alpha $$-Hermite BV functions and the rank-one theorem for $$\mathcal{B}\mathcal{V}_{{\mathcal {H}_{\alpha }}}$$	2023	Xixiang Du Yu Liu He Wang
+	Boundedness of fractional heat semigroups generated by degenerate Schrödinger operators	2023	Zhiyong Wang Pengtao Li Yu Liu
+	Boundedness for Littlewood-Paley functions on weighted Morrey-type spaces related to certain nonnegative potentials	2023	N. Zhao Jiang Zhou Yu Liu
+	BV Capacity and Sobolev Capacity for the Laguerre Operator	2023	He Wang Yu Liu
+	Boundedness of square functions related with fractional Schrödinger semigroups on stratified Lie groups	2023	Zhiyong Wang Kai Zhao Pengtao Li Yu Liu
+	Sobolev and Variational Capacities in the Hermite Setting and Their Applications	2022	Jizheng Huang Pengtao Li Yu Liu
+ PDF Chat	Capacity and the Corresponding Heat Semigroup Characterization from Dunkl-Bounded Variation	2021	Xiang-Ling Meng Yu Liu Xiang-Yun Xie
+	The $$\infty $$-capacity and Faber–Krahn inequality on Grushin spaces	2021	Guoliang Li Yu Liu
+	Extension of Campanato–Sobolev type spaces associated with Schrödinger operators	2020	Jizheng Huang Pengtao Li Yu Liu
+	A Novel Multimodal Approach for Hybrid Brain–Computer Interface	2020	Zhe Sun Zihao Huang Feng Duan Yu Liu
+ PDF Chat	Area Integral Characterization of Hardy space H1L related to Degenerate Schrödinger Operators	2019	Jizheng Huang Pengtao Li Yu Liu
+	BMO-type estimates of Riesz transforms associated with generalized Schrödinger operators	2019	Yu Liu Qi Shuai
+	Bilinear operators associated with generalized Schrödinger operators	2018	Nan Hu Yu Liu
+	Regularity properties of the heat kernel and area integral characterization of Hardy space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="script">L</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math> related to degenerate Schrödinger operators	2018	Jizheng Huang Pengtao Li Yu Liu
+	A note on BV capacities on Grushin spaces	2018	Guoliang Li Yu Liu
+ PDF Chat	Commutators associated with Schrödinger operators on the nilpotent Lie group	2017	Tianzhen Ni Yu Liu
+	Functional capacities on the Grushin space $${\mathbb {G}}^n_\alpha $$ G α n	2017	Yu Liu Jie Xiao
+	Boundedness for Riesz Transforms Related to Schr?dinger Operators and Their Commutators on Weighted Morrey Spaces	2017	Yu Liu
+ PDF Chat	Poisson semigroup, area function, and the characterization of Hardy space associated to degenerate Schrödinger operators	2016	Jizheng Huang Pengtao Li Yu Liu
+ PDF Chat	Some estimates for commutators of Riesz transform associated with Schrödinger type operators	2016	Yu Liu Jing Zhang Jielai Sheng Lijuan Wang
+	BV Capacity on Generalized Grushin Plane	2016	Yu Liu
+ PDF Chat	Higher order commutators of Riesz transforms related to Schrödinger operators	2014	Yuanting Wang Yu Liu
+ PDF Chat	Boundedness for Riesz transform associated with Schrödinger operators and its commutator on weighted Morrey spaces related to certain nonnegative potentials	2014	Yu Liu Lijuan Wang
+	Some estimates for commutators of Riesz transforms associated with Schrödinger operators	2014	Yu Liu Jielai Sheng
+ PDF Chat	Molecular Characterization of Hardy Spaces Associated with Twisted Convolution	2014	Jizheng Huang Yu Liu
+ PDF Chat	Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators	2013	Yu Liu Lijuan Wang Jianfeng Dong
+ PDF Chat	Weighted Endpoint Estimates for Commutators of Riesz Transforms Associated with Schrödinger Operators	2013	Yu Liu Jielai Sheng Lijuan Wang
+ PDF Chat	The Higher Order Riesz Transform and<i>BMO</i>Type Space Associated with Schrödinger Operators on Stratified Lie Groups	2013	Yu Liu Jianfeng Dong
+	Some estimates for the Schrödinger type operators with nonnegative potentials	2012	Yu Liu Jianfeng Dong
+	L p estimates for the Schrödinger type operators	2011	Yu Liu Jizheng Huang
+	L(superscript p) Estimates for the Schrödinger Type Operators	2011	Yu Liu Jizheng Huang
+	Hardy spaces associated with Schrodinger operators on the Heisenberg group	2011	Chin-Cheng Lin Heping Liu Yu Liu
+ PDF Chat	Bilinear operators associated with Schrödinger operators	2011	Chin-Cheng Lin Ying‐Chieh Lin Heping Liu Yu Liu
+	Commutators of BMO functions and degenerate Schrödinger operators with certain nonnegative potentials	2010	Yu Liu
+ PDF Chat	L<sup>p</sup>ESTIMATES FOR SCHRÖDINGER TYPE OPERATORS ON THE HEISENBERG GROUP	2010	Yu Liu
+	Some estimates of Schrödinger type operators on the Heisenberg group	2010	Yu Liu Jizheng Huang Dongmei Xie
+	Hardy spaces HL1(Rn) associated to Schrödinger Type Operators (- )2+V2	2010	Jun Cao Yu Liu Dachun Yang
+	WAVELETS WITH VANISHING MOMENTS ON THE HEISENBERG GROUP	2010	Yu Liu Lizhong Peng
+	Cascade algorithm and multiresolution analysis on the Heisenberg group	2010	Yu Liu
+	Riesz Transform Associated With Schrdinger Operators on the Heisenberg Group	2010	Yu Liu
+	Multiresolution analysis, self-similar tilings and Haar wavelets on the Heisenberg group	2009	Heping Liu Yu Liu Haihui Wang
+	Some characterizations of weighted Hardy spaces	2009	Jizheng Huang Yu Liu
+	Endpoint Estimates for the Fraction Commutators of Marcinkiewicz Integrals	2008	Yu Liu
+	Lipschitz continuity of refinable functions on the Heisenberg group	2007	Yu Liu Mei Yu
+	Schrdinger Operator on the Heisenberg Group	2006	Yu Liu
+	Inequalities for the Hadamard Product of Positive Semidefinite Matrices	2006	Yu Liu
+	The Uniform Boundness of the Upper Semi-continuous Operator Family in Quasi-normed Space	2003	Yu Liu
+	Rotundity of Orlicz-Bochner Space with Luxemburg Norm	2003	Yu Liu
+	THE STUDY OF THE STABILITY OF FRAMES AND ATOMIC DECOMPOSITON FOR BANACH SPACES	2002	Yu Liu
+	THE KOTHE DUALS OF FUNCTION SPACES OF SEQUENTIALLY TYPE	2001	Yu Liu
+	ATTRACTORS OF NONAUTONOMOUS SCHR?DINGER EQUATIONS	2001	Yu Liu
+	A Munkholm Type of Theorem for Maps from a Sphere into a Smooth Manifold	2000	Yu Liu
+	ASYMPOTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF MICHAELIS-MENTON TYPE DIFFERENCE EQUAITON	2000	Yu Liu

Common Coauthors

Coauthor	Papers Together
Jizheng Huang	10
Pengtao Li	9
Lijuan Wang	4
Jianfeng Dong	3
Zhiyong Wang	3
Jielai Sheng	3
Heping Liu	2
N. Zhao	2
He Wang	2
Nan Zhao	2
Haihui Wang	2
Lizhong Peng	1
He Wang	1
Zihao Huang	1
Guoliang Li	1
Zhiyong Wang	1
Guoliang Li	1
Heping Liu	1
Dongmei Xie	1
Xixiang Du	1
Jun Cao	1
Kai Zhao	1
Qi Shuai	1
Jing Zhang	1
Chin-Cheng Lin	1
Dachun Yang	1
Xiang-Yun Xie	1
Chin-Cheng Lin	1
Ying‐Chieh Lin	1
Guiyang Liu	1
Feng Duan	1
Jiang Zhou	1
He Wang	1
Zhe Sun	1
Jie Xiao	1
Tianzhen Ni	1
Mei Yu	1
Nan Hu	1
Xiang-Ling Meng	1
Yuanting Wang	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	$L^p$ estimates for Schrödinger operators with certain potentials	1995	Zhongwei Shen	18
+ PDF Chat	Hardy space $H^1$ associated to Schrödinger operator with potential satisfying reverse Hölder inequality	1999	Jacek Dziubański Jacek Zienkiewicz	14
+	Localized Hardy spaces 𝐻¹ related to admissible functions on RD-spaces and applications to Schrödinger operators	2010	Dachun Yang Yuan Zhou	10
+	EstimationsLpdes opérateurs de Schrödinger sur les groupes nilpotents	1999	Hong-Quan Li	8
+	Commutators of Riesz Transforms Related to Schrödinger Operators	2010	Bruno Bongioanni Eleonor Harboure Oscar Salinas	8
+	The sharp Sobolev and isoperimetric inequalities split twice	2006	Jie Xiao	7
+ PDF Chat	<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:math> boundedness of commutators of Riesz transforms associated to Schrödinger operator	2007	Zihua Guo Pengtao Li Lizhong Peng	7
+	The BV-capacity in metric spaces	2010	Heikki Hakkarainen Juha Kinnunen	7
+	Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals	2002	Elias M. Stein Timothy S Murphy	6
+ PDF Chat	Localized Morrey-Campanato spaces on metric measure spaces and applications to Schrüdinger operators	2010	Dachun Yang Dongyong Yang Yuan Zhou	6
+	The uncertainty principle	1983	Charles Fefferman	6
+	Commutators of Calderón-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrödinger operators	2012	Yu Liu Jizheng Huang Jianfeng Dong	6
+ PDF Chat	Hp spaces of several variables	1972	Charles Fefferman E. M. Stein	6
+	BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality	2004	Jacek Dziubański Gustavo Garrigós Teresa Martı́nez J. L. Torrea Jacek Zienkiewicz	6
+ PDF Chat	$L^p$ Estimates for Some Schrödinger Type Operators and a Calderóon-Zygmund Operator of Schrödinger Type	2007	Satoko Sugano	6
+	Endpoint Properties of Localized Riesz Transforms and Fractional Integrals Associated to Schrödinger Operators	2009	Dachun Yang Dongyong Yang Yuan Zhou	6
+ PDF Chat	Localized BMO and BLO spaces on RD-spaces and applications to Schrödinger operators	2010	Dachun Yang Dongyong Yang Yuan Zhou	6
+	Factorization Theorems for Hardy Spaces in Several Variables	1976	Ronald R. Coifman Richard Rochberg Guido Weiss	5
+	Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces	1996	Nicola Garofalo Duy-Minh Nhieu	5
+ PDF Chat	ENDPOINT ESTIMATES FOR COMMUTATORS OF RIESZ TRANSFORMS ASSOCIATED WITH SCHRÖDINGER OPERATORS	2010	Pengtao Li Lizhong Peng	5
+	Functions of bounded variation on “good” metric spaces	2003	Michele Miranda	5
+	Some Estimates of Higher Order Riesz Transform Related to Schrödinger Type Operators	2009	Yu Liu Jianfeng Dong	5
+	BV Capacity on Generalized Grushin Plane	2016	Yu Liu	5
+	Boundedness for some Schrödinger type operators on Morrey spaces related to certain nonnegative potentials	2009	Lin Tang Jianfeng Dong	5
+	Capacity & perimeter from $$\alpha $$-Hermite bounded variation	2020	Jizheng Huang Pengtao Li Yu Liu	5
+	Conductor and capacitary inequalities for functions on topological spaces and their applications to Sobolev-type imbeddings	2004	Vladimir Maz’ya	4
+	None	2002	Luigi Ambrosio	4
+	Orlicz-Hardy spaces associated with operators	2008	Renjin Jiang Dachun Yang Yuan Zhou	4
+ PDF Chat	ORLICZ–HARDY SPACES ASSOCIATED WITH OPERATORS SATISFYING DAVIES–GAFFNEY ESTIMATES	2011	Renjin Jiang Dachun Yang	4
+ PDF Chat	Isoperimetric inequality in the Grushin plane	2004	Roberto Monti Daniele Morbidelli	4
+ PDF Chat	Weighted norm inequalities for Schrödinger type operators	2013	Lin Tang	4
+	Functional capacities on the Grushin space $${\mathbb {G}}^n_\alpha $$ G α n	2017	Yu Liu Jie Xiao	4
+ PDF Chat	Lebesgue points and capacities via boxing inequality in metric spaces	2008	Juha Kinnunen Riikka Korte Nageswari Shanmugalingam Heli Tuominen	4
+	Regularity and capacity for the fractional dissipative operator	2015	Renjin Jiang Jie Xiao Dachun Yang Zhichun Zhai	4
+ PDF Chat	L<sup>p</sup>ESTIMATES FOR SCHRÖDINGER TYPE OPERATORS ON THE HEISENBERG GROUP	2010	Yu Liu	4
+ PDF Chat	Commutators of BMO functions and singular integral operators with non-smooth kernels	2003	Xuan Thinh Duong Lixin Yan	4
+	Weakly Differentiable Functions	1989	William P. Ziemer	4
+	Duality of Hardy and BMO spaces associated with operators with heat kernel bounds	2005	Xuan Thinh Duong Lixin Yan	4
+ PDF Chat	On the relation between elliptic and parabolic Harnack inequalities	2001	Waldemar Hebisch Laurent Saloff‐Coste	4
+ PDF Chat	Note on $H\sp 1$ spaces related to degenerate Schrödinger operators	2005	Jacek Dziubański	4
+ PDF Chat	Hardy spaces H L p (ℝ n ) associated with operators satisfying k-Davies-Gaffney estimates	2012	Jun Cao Dachun Yang	4
+	Commutators of BMO functions and degenerate Schrödinger operators with certain nonnegative potentials	2010	Yu Liu	4
+ PDF Chat	Maximal inequalities and Riesz transform estimates on L^p spaces for Schrödinger operators with nonnegative potentials	2007	Pascal Auscher Besma Ben Ali	4
+	Surface measures in Carnot-Carath�odory spaces	2001	Roberto Monti Francesco Serra Cassano	4
+ PDF Chat	Mean oscillation and commutators of singular integral operators	1978	Svante Janson	4
+	Function Spaces and Potential Theory	1996	David R. Adams Lars Inge Hedberg	4
+ PDF Chat	Estimates for the Operators $V^{\alpha}(-\Delta+V)^{-\beta}$ and $V^{\alpha}\nabla(-\Delta+V)^{-\beta}$ with Certain Non-negative Potentials $V$	1998	Satoko Sugano	4
+	Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic operators with positive potentials	2000	Kazuhiro Kurata Satoko Sugano	4
+ PDF Chat	Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators	2013	Yu Liu Lijuan Wang Jianfeng Dong	4
+	Harmonic analysis for some Schrödinger type operators	1993	Jiaping Zhong	4