Borderline weighted estimates for commutators of singular integrals

Pérez, Carlos; Rivera-Rı́os, Israel P.

doi:10.1007/s11856-017-1454-6

Cited by 11 publications

(7 citation statements)

References 23 publications

(38 reference statements)

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“…In [37] C. Pérez an G. Pradolini obtained an endpoint estimate for conmutators with arbitrary weights, and later on, C. Pérez and the second author [38] obtained a quantitative version of that result that reads as follows…”

Section: Some Particular Cases Of Interest and Applications Revisitedmentioning

confidence: 99%

Sparse and weighted estimates for generalized Hörmander operators and commutators

Ibañez-Firnkorn

Rivera-Rı́os

2019

Monatsh Math

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In this paper a pointwise sparse domination for generalized Hörmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in [24]. Relying upon that sparse domination a number of quantitative estimates are derived. Some of them are improvements and complementary results to those contained in a series of papers due to M. Lorente, J. M. Martell, C. Pérez, S. Riveros and A. de la Torre [30,29,28]. Also the quantitative endpoint estimates in [24] are extended to iterated commutators. Other results that are obtained in this work are some local exponential decay estimates for generalized Hörmander operators in the spirit of [34] and some negative results concerning Coifman-Fefferman estimates for a certain class of kernels satisfying particular generalized Hörmander conditions.2000 Mathematics Subject Classification. 42B20, 42B25.

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Section: Some Particular Cases Of Interest and Applications Revisitedmentioning

confidence: 99%

Sparse and weighted estimates for generalized Hörmander operators and commutators

Ibañez-Firnkorn

Rivera-Rı́os

2019

Monatsh Math

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“…Consider now the commutator [b, T ] of T with a BMO function b. The following analogue of (1.4) was recently obtained by the third author and C. Pérez [31]: for all 0 < ε ≤ 1,…”

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confidence: 99%

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

Lerner

Ombrosi

Rivera-Rı́os

2017

Advances in Mathematics

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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 ∈ BM O, we improve several weighted weak type bounds for [b, T ]. If b belongs to the weighted BM O, we obtain a quantitative form of the two-weighted bound for [b, T ] due to Bloom-Holmes-Lacey-Wick.2010 Mathematics Subject Classification. 42B20, 42B25.

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“…Subsequently, Lerner et al [37] extended the results to the iterated commutator and established the necessary conditions for a rather wider class of operators. For more applications of sparse operators to commutators, see [1,11,28,43,45,46,48], and references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%