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.
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页码：126 / 138
页数：13
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