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.

引用

页码：1064 / 1083

页数：20

共 43 条

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[42] ALMOST EVERYWHERE CONVERGENCE FOR MODIFIED BOCHNER-RIESZ MEANS AT THE CRITICAL INDEX FOR p ≥ 2
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[J]. PACIFIC JOURNAL OF MATHEMATICS, 2017, 286 (02) : 257 - 275
[43] Bochner-Riesz Means on Hardy Spaces Associated with Ball Quasi-Banach Function Spaces
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