Multilinear extrapolation and applications to the bilinear Hilbert transform

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:357

Article

Jesus Carro, Maria²  Grafakos, Loukas³  Maria Martell, Jose¹  Soria, Fernando⁴ 

[1] CSIC, UAM, UC3M, UCM,Inst Ciencias Matemat, E-28006 Madrid, Spain

[2] Univ Barcelona, Dept Matemat Aplicada & Anal, E-08071 Barcelona, Spain

[3] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[4] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

关键词: Multilinear extrapolation;    Restricted weak type estimates;    (epsilon, delta)-atomic operators;    Galb;    Bilinear Hilbert transform;   

DOI  :  10.1016/j.jmaa.2009.04.021

来源: Elsevier

【 摘 要 】

We present two extrapolation methods for multi-sublinear operators that allow us to derive estimates for general functions from the corresponding estimates on characteristic functions. Of these methods, the first is applicable to general multi-sublinear operators while the second requires working with the so-called (epsilon, delta)-atomic operators. Among the applications, we discuss some new endpoint estimates for the bilinear Hilbert transform. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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