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 |
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Pages (from-to) | 153-181 |
Number of pages | 29 |
Journal | Advances in Mathematics |
Volume | 319 |
DOIs | |
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