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

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

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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 languageEnglish
Pages (from-to)153-181
Number of pages29
JournalAdvances in Mathematics
StatePublished - 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.


  • Calderón–Zygmund operators
  • Commutators
  • Sparse operators
  • Weighted inequalities


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