Pseudodifferential operators with homogeneous symbols.

Loukas Grafakos, Rodolfo H. Torres

Type: Article

Publication Date: 1999-09-01

Citations: 31

DOI: https://doi.org/10.1307/mmj/1030132409

Abstract

We prove boundedness of pseudodifferential operators with symbols satisfying the conditions |∂ ξ ∂ xa(x, ξ)| ≤ Cβ,γ |ξ|m−|β|+|γ| on homogeneous Besov-Lipschitz and Triebel-Lizorkin spaces

Locations

The Michigan Mathematical Journal - View - PDF

Similar Works

Action	Title	Year	Authors
+	On the boundedness of pseudo-differential operators on Triebel–Lizorkin and Besov spaces	2018	Bae Jun Park
+	Continuity in Quasi-homogeneous Sobolev Spaces for Pseudo-differential Operators with Besov Symbols	2007	Gianluca Garello Alessandro Morando
+	Bilinear pseudodifferential operators with forbidden symbols on Lipschitz and Besov spaces	2003	Árpád Bényi
+	Continuity in Weighted Besov Spaces for Pseudodifferential Operators with Non-regular Symbols	2005	Gianluca Garello Alessandro Morando
+	Boundedness of Product Type Pseudodifferential Operators on Spaces of Besov Type	1987	Masao Yamazaki
+	Continuity of non-regular pseudodifferential operators on variable Triebel–Lizorkin spaces	2019	Douadi Drihem Wafa Hebbache
+ PDF Chat	Nonregular Pseudo-Differential Operators	1996	Jürgen Marschall
+ PDF Chat	Boundedness of non regular pseudodifferential operators on variable Besov spaces	2016	Douadi Drihem Wafa Hebbache
+ PDF Chat	Boundedness of non regular pseudodifferential operators on variable Besov spaces	2022	Douadi Drihem Douadi Drihem W. Hebbache
+ PDF Chat	$$L^p$$ Continuity and Microlocal Properties for Pseudodifferential Operators	2019	Gianluca Garello Alessandro Morando
+	Boundedness of multilinear pseudo-differential operators with $$S_{0,0}$$ class symbols on Besov spaces	2024	Naoto Shida
+	Sharp estimates for pseudo-differential operators of type (1,1) on Triebel-Lizorkin and Besov spaces	2017	Bae Jun Park
+ PDF Chat	Boundedness of pseudo‐differential operators of type (0,0) on Triebel–Lizorkin and Besov spaces	2019	Bae Jun Park
+ PDF Chat	Estimates of bilinear pseudodifferential operators associated to bilinear Hörmander classes in Besov and Triebel–Lizorkin spaces with variable exponents	2018	Jingshi Xu Jinlai Zhu
+	Pseudodifferential operators on localized Besov spaces	2013	Madani Moussai Salah Eddine Allaoui
+ PDF Chat	Mapping properties of operator-valued pseudo-differential operators	2019	Runlian Xia Xiao Xiong
+	Boundedness of pseudodifferential operators in Hölder-Zygmund spaces of variable order	2014	V. D. Kryakvin
+	Pseudodifferential operators with rough symbols	2007	Atanas Stefanov
+	Pseudodifferential operators in ᵖ(ℝⁿ)	2004	Ryuichi Ashino Michihiro Nagase Rémi Vaillancourt
+	Sharp estimates for pseudo-differential operators of type (1,1) on Triebel-Lizorkin and Besov spaces	2017	Bae Jun Park

Works That Cite This (31)

Action	Title	Year	Authors
+	Molecular decomposition of anisotropic homogeneous mixed-norm spaces with applications to the boundedness of operators	2017	Galatia Cleanthous Athanasios G. Georgiadis Morten Nielsen
+	Characterizations of $$B^u_\omega $$ type Morrey–Triebel–Lizorkin spaces with variable smoothness and integrability	2024	Shengrong Wang Pengfei Guo Jingshi Xu
+ PDF Chat	Molecular decomposition and Fourier multipliers for holomorphic Besov and Triebel–Lizorkin spaces	2019	Galatia Cleanthous Athanasios G. Georgiadis Morten Nielsen
+	A framework of Besov–Triebel–Lizorkin type spaces via ball quasi-Banach function sequence spaces I: real-variable characterizations	2024	Jingsong Sun Dachun Yang Wen Yuan
+	New applications of Besov-type and Triebel–Lizorkin-type spaces	2009	Yoshihiro Sawano Dachun Yang Wen Yuan
+ PDF Chat	Dual Properties of Triebel–Lizorkin-Type Spaces and their Applications	2011	Dachun Yang Wen Yuan
+	Decompositions of Besov–Hausdorff and Triebel–Lizorkin–Hausdorff spaces and their applications	2010	Wen Yuan Yoshihiro Sawano Dachun Yang
+	Function spaces of Besov-type and Triebel-Lizorkin-type — a survey	2013	Dachun Yang Wen Yuan
+	Musielak–Orlicz Besov-type and Triebel–Lizorkin-type spaces	2013	Dachun Yang Wen Yuan Ciqiang Zhuo
+	Matrix-weighted Besov-type and Triebel–Lizorkin-type spaces III: characterizations of molecules and wavelets, trace theorems, and boundedness of pseudo-differential operators and Calderón–Zygmund operators	2024	Fan Bu Tuomas Hytönen Dachun Yang Wen Yuan

Works Cited by This (16)

Action	Title	Year	Authors
+ PDF Chat	Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires	1981	Jean-Michel Bony
+	New thoughts on Besov spaces	1976	Jaak Peetre
+	Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals	2002	Elias M. Stein Timothy S Murphy
+	Theory of function spaces	1983	Hans Triebel
+	Continuity Properties of Pseudodifferential Operators of Type 1,1	1990	Rodolfo H. Torres
+	Singular Integral Operators and Differential Equations	1989	A. P. Calderón A. Zygmund
+	A discrete transform and decompositions of distribution spaces	1990	Michael Frazier Björn Jawerth
+	Une algebre maximale d'operateurs pseudo-differentiels d'operateurs pseudo-differentiels	1988	Gérard Bourdaud
+	Boundedness results for operators with singular kernels on distribution spaces	1991	Rodolfo H. Torres
+	Régularité des solutions des équations aux dérivées partielles non linéaires	2006	Yves Meyer