On fundamental harmonic analysis operators in certain Dunkl and Bessel settings

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:412

Article

Castro, Alejandro J.¹  Szarek, Tomasz Z.² 

[1] Univ La Laguna, Dept Anal Matemat, San Cristobal la Laguna 38271, Sta Cruz De Ten, Spain

[2] Polish Acad Sci, Inst Matemat, PL-00956 Warsaw, Poland

关键词: Dunkl Laplacian;    Bessel Laplacian;    Dunkl transform;    Hankel transform;    Maximal operator;    Square function;    Multiplier;    Riesz transform;    Lusin area integral;    Calderon-Zygmund operator;   

DOI  :  10.1016/j.jmaa.2013.11.020

来源: Elsevier

【 摘 要 】

We consider several harmonic analysis operators in the multi-dimensional context of the Dunk! Laplacian with the underlying group of reflections isomorphic to Z(2)(n) (also negative values of the multiplicity function are admitted). Our investigations include maximal operators, g-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes transform type. Using the general Calderon-Zygmund theory we prove that these objects are bounded in weighted L-p spaces, 1 < p < infinity, and from L-1 into weak L-1. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free