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Improved A1−A∞ and Related Estimates for Commutators of Rough Singular Integrals

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  06 August 2018

Israel P. Rivera-Ríos
Israel P. Rivera-Ríos*
Affiliation:
Universidad del País Vasco/Euskal Herriko Unibertsitatea, Departamento de Matematicas/Matematika saila, Apdo. 644, 48080 Bilbao, Spain BCAM–Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain (petnapet@gmail.com)
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Abstract

An A1−A∞ estimate, improving on a previous result for [b, TΩ] with $\Omega \in L^{infty}({\open S}^{n - 1})$ and b∈BMO is obtained. A new result in terms of the A∞ constant and the one supremum Aq−A∞exp constant is also proved, providing a counterpart for commutators of the result obtained by Li. Both of the preceding results rely upon a sparse domination result in terms of bilinear forms, which is established using techniques from Lerner.

Keywords

rough singular integralscommutatorssparse boundsweights

MSC classification

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 1069 - 1086
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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