ON LITTLEWOOD-PALEY FUNCTIONS ASSOCIATED WITH THE DUNKL OPERATOR

被引：3

作者：

Liao, Jianquan ^{[1
]}

Zhang, Xiaoliang ^{[2
]}

Li, Zhongkai ^{[3
]}

机构：

[1] Guangdong Univ Educ, Dept Math, Guangzhou 510303, Guangdong, Peoples R China

[2] Capital Normal Univ, Dept Math, Beijing 100048, Peoples R China

[3] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2017年 / 96卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Littlewood-Paley function; Dunkl operator; lambda-Poisson integral; lambda-Hilbert transform; Dunkl transform;

D O I：

10.1017/S0004972717000223

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A Littlewood-Paley operator associated with the reflection part of the Dunkl operator is introduced and proved to be of type (p; p) for 1 < p < infinity, based on boundedness of a generalised vector-valued singular integral. This fills a gap for 2 < p < infinity concerning the boundedness of a g-function in the Dunkl setting. The paper also supplies new proofs for 1 < p < infinity on the (p; p) boundedness of various g-functions associated with the Dunkl operator.

引用

页码：126 / 138

页数：13

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