Maximal bilinear singular integral operators associated with dilations of planar sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:332

Article

Diestel, Geoff ; Grafakos, Loukas

关键词: Bilinear operators;    Bilinear Hilbert transform;    lacunary almost everywhere convergence;   

DOI  :  10.1016/j.jmaa.2006.10.094

来源: Elsevier

【 摘 要 】

We obtain square function estimates and bounds for maximal singular integral operators associated with bilinear multipliers given by characteristic functions of dyadic dilations of certain planar sets. As a consequence, we deduce pointwise almost everywhere convergence for lacunary partial sums of bilinear Fourier series with respect to methods of summation determined by the corresponding planar sets. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free