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New bounds for bilinear Calderon-Zygmund operators and applications

Journal article
Authors Wendolín Damián
Mahdi Hormozi
Kangwei Li
Published in Revista Matematica Iberoamericana
Volume 34
Pages 1177-1210
ISSN 0213-2230
Publication year 2018
Published at Department of Mathematical Sciences
Pages 1177-1210
Language en
Links https://doi.org/10.4171/RMI/1021
Keywords Commutators, Dini condition, Domination theorem, Fourier multipliers, Multilinear Calderón-Zygmund operators, Square functions
Subject categories Mathematical Analysis, Signal Processing, Control Engineering

Abstract

© European Mathematical Society. In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calderón-Zygmund operators with Dini-continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hytönen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple A∞ constants inspired in the Fujii-Wilson and Hrusčěv classical constants. These estimates have many new applications including mixed bounds for multilinear Calderón-Zygmund operators and their commutators with BMO functions, square functions and multilinear Fourier multipliers.

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Utskriftsdatum: 2019-10-20