Kato-Ponce type inequality for bilinear pseudo-differential operators of $S_{0, 0}$-type in the scale of Besov spaces

DOI10.1090/PROC/15650zbMath1475.35435arXiv2010.14690OpenAlexW3158660541MaRDI QIDQ4957660

Naoto Shida

Publication date: 9 September 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.14690

zbMATH Keywords

Besov spacesbilinear pseudo-differential operatorsbilinear Hörmander symbol classesKato-Ponce type inequality

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Function spaces arising in harmonic analysis (42B35) Multipliers for harmonic analysis in several variables (42B15)

Related Items (2)

Boundedness of bilinear pseudo‐differential operators with BS0,0m$BS^{m}_{0,0}$ symbols on Sobolev spaces ⋮ Boundedness of multilinear pseudo-differential operators with \(S_{0,0}\) class symbols on Besov spaces

Cites Work

• Theory of function spaces
• Pseudo-differential operators on Besov spaces
• Bilinear pseudo-differential operators with symbols in \(BS^m_{1,1}\) on Triebel-Lizorkin spaces
• Almost orthogonality and a class of bounded bilinear pseudodifferential operators
• Bilinear pseudo-differential operators with exotic symbols
• Boundedness of multilinear pseudo-differential operators of \(S_{0,0}\)-type in \(L^2\)-based amalgam spaces
• Bilinear pseudo-differential operators with exotic class symbols of limited smoothness
• On the ranges of bilinear pseudo-differential operators of \(S_{0,0}\)-type on \(L^2 \times L^2\)
• Multilinear pseudodifferential operators beyond Calderón-Zygmund theory
• Bilinear Hörmander classes of critical order and Leibniz-type rules in Besov and local Hardy spaces
• The Kato-Ponce Inequality
• Commutator estimates and the euler and navier-stokes equations
• Symbolic Calculus and the Transposes of Bilinear Pseudodifferential Operators
• Classical and Multilinear Harmonic Analysis
• On the Hormander classes of bilinear pseudodifferential operators II
• Calderon-Vaillancourt--type theorem for bilinear operators
• A Class of Bounded Pseudo-Differential Operators

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