On pointwise and weighted estimates for commutators of Calderón–Zygmund operators

Andrei K. Lerner; Sheldy Ombrosi; Israel P. Rivera-Ríos

doi:10.1016/j.aim.2017.08.022

On pointwise and weighted estimates for commutators of Calderón–Zygmund operators

Andrei K. Lerner, Sheldy Ombrosi, Israel P. Rivera-Ríos

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

69 Scopus citations

Abstract

In recent years, it has been well understood that a Calderón–Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar pointwise estimate for the commutator [b,T] with a locally integrable function b. This result is applied into two directions. If b∈BMO, we improve several weighted weak type bounds for [b,T]. If b belongs to the weighted BMO, we obtain a quantitative form of the two-weighted bound for [b,T] due to Bloom–Holmes–Lacey–Wick.

Original language	English
Pages (from-to)	153-181
Number of pages	29
Journal	Advances in Mathematics
Volume	319
DOIs	https://doi.org/10.1016/j.aim.2017.08.022
State	Published - 15 Oct 2017

Bibliographical note

Funding Information:
The third author was supported by the Basque Government through the BERC 2014–2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and also through the projects MTM2014-53850-P and MTM2012-30748.

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

Calderón–Zygmund operators
Commutators
Sparse operators
Weighted inequalities

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10.1016/j.aim.2017.08.022

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AU - Ombrosi, Sheldy

AU - Rivera-Ríos, Israel P.

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KW - Sparse operators

KW - Weighted inequalities

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On pointwise and weighted estimates for commutators of Calderón–Zygmund operators

Abstract

Bibliographical note

Keywords

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