Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach

Abstract

We present a unified method to obtain weighted estimates of linear and multilinear commutators with BMO functions, that is amenable to a plethora of operators and functional settings. Our approach elaborates on a commonly used Cauchy integral trick, recovering many known results but yielding also numerous new ones.

v3: addition of appendix which includes quantitative weighted estimates for commutators of the bilinear Hilbert transform

References in corpus (3)

• Extrapolation for multilinear Muckenhoupt classes and applications to the bilinear Hilbert transform
• Limited range multilinear extrapolation with applications to the bilinear Hilbert transform
• Two-weight inequalities for multilinear commutators

Cited by in corpus (15)

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• End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications
• A revisit on the compactness of commutators
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• A class of multilinear bounded oscillation operators on measure spaces and applications
• A Survey on Function Spaces of John--Nirenberg Type
• Two-weight inequalities for multilinear commutators
• Extrapolation of compactness on weighted spaces
• Extrapolation of compactness on weighted spaces II: Off-diagonal and limited range estimates
• Extrapolation of compactness on Banach function spaces
• XMO and Weighted Compact Bilinear Commutators
• Two-weight extrapolation on function spaces and applications
• Extrapolation of compactness on weighted Morrey spaces
• Weighted Estimates of Singular Integrals and Commutators in the Zygmund Dilation Setting
• On the weak boundedness of multilinear Littlewood--Paley functions