WEIGHTED HERZ SPACE ESTIMATES FOR HAUSDORFF OPERATORS ON THE HEISENBER GGROUP

被引：32
|
作者：
Ruan, Jianmiao [1 ]
Fan, Dashan [2 ]
Wu, Qingyan [3 ]
机构：
[1] Zhejiang Int Studies Univ, Dept Math, Hangzhou 310012, Zhejiang, Peoples R China
[2] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA
[3] Linyi Univ, Dept Math, Linyi 276005, Peoples R China
来源：
BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2017年 / 11卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Hausdorff operator; Herz space; Heisenberg group; weight; HARDY-SPACES; BOUNDEDNESS;
D O I：
10.1215/17358787-2017-0004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we study the Hausdorff operator, defined via a general linear mapping A, on weighted Herz spaces in the setting of the Heisenberg group. Under some assumptions on the mapping A, we establish its sharp boundedness on power-weighted Herz spaces and power-weighted Lebesgue spaces in the Heisenberg group. Our proof is heavily based on the block decomposition of the Herz space, which is quite different from any other function spaces. Our results extend and improve some existing theorems.
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页码：513 / 535
页数：23
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