Necessary and sufficient conditions for the bounds of the Calderón type commutator for the Littlewood-Paley operator

DOI10.1016/j.na.2015.10.017zbMath1329.42012OpenAlexW2179988575MaRDI QIDQ898372

Ding, Yong, Yan-ping Chen

Publication date: 8 December 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2015.10.017

zbMATH Keywords

rough kernelLipschitz functionLittlewood-Paley operatorCalderón type commutator

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25)

Related Items (5)

\(L^2(\mathbb{R}^n)\) boundedness for Calderón commutator with rough variable kernel ⋮ Quantitative weighted bounds for Calderón commutators with rough kernels ⋮ Vector‐valued singular integral operators with rough kernels ⋮ Necessary and sufficient conditions for the bounds of the commutator of a Littlewood-Paley operator with fractional differentiation ⋮ \(L^p(\mathbb{R}^d)\) boundedness for the Calderón commutator with rough kernel

Cites Work

• Estimates for translation invariant operators in \(L^p\) spaces
• On Marcinkiewicz integral operators with rough kernels
• Commutators of Littlewood-Paley operators
• Maximal and singular integral operators via Fourier transform estimates
• Boundedness of singular integral operators of Calderón type. V
• Polynomial growth estimates for multilinear singular integral operators
• Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials
• A note on Marcinkiewicz integral operators.
• On the commutator of the Marcinkiewicz integral.
• \(L^p\) bounds for the function of Marcinkiewicz.
• On commutators of Marcinkiewicz integrals with rough kernel
• Operators with rough singular kernels
• CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS
• On the Functions of Littlewood-Paley, Lusin, and Marcinkiewicz
• A note on the Marcinkiewicz integral
• On Commutators of Singular Integrals and Bilinear Singular Integrals
• Cauchy integrals on Lipschitz curves and related operators
• Weighted boundedness for a class of rough Marcinkiewicz integrals
• Classical and Multilinear Harmonic Analysis
• L^p estimates for the commutators of Marcinkiewicz integrals with kernels belonging to certain block spaces
• COMMUTATORS OF SINGULAR INTEGRAL OPERATORS
• On the function of Marcinkiewicz
• \(L^p\)-boundedness of Marcinkiewicz integrals with Hardy space function kernels
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Necessary and sufficient conditions for the bounds of the Calderón type commutator for the Littlewood-Paley operator