WEAK BOUNDEDNESS OF OPERATOR-VALUED BOCHNER-RIESZ MEANS FOR THE DUNKL TRANSFORM

被引：1
|
作者：
Wang, Maofa [1 ]
Xu, Bang [1 ]
Hu, Jian [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
来源：
BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2018年 / 12卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Dunkl transform; von Neumann algebra; Bochner-Riesz means; WEIGHTED VARIATION INEQUALITIES; DIFFERENTIAL-OPERATORS; HARMONIC-ANALYSIS; BEHAVIOR;
D O I：
10.1215/17358787-2018-0012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider operator-valued Bochner-Riesz means with weight function h(k)(2) under a finite reflection group for the Dunkl transform. We establish the maximal inequality of the weighted Hardy-Littlewood maximal function, and we apply it to the maximal inequality of operator-valued Bochner-Riesz means B-R(delta) (h(k)(2); f) (x) for delta > lambda(k) := d-1/2 + Sigma(d)(j-1) k(j). Furthermore, we also obtain the corresponding pointwise convergence theorem.
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页码：1064 / 1083
页数：20
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