Hausdorff Operators on the Heisenberg Group

被引：18
作者：
Guo, Jiu Hua [1 ]
Sun, Li Jing [2 ]
Zhao, Fa You [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2015年 / 31卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Hausdorff operator; Heisenberg group; multilinear; sharp estimate; HARDY;
D O I：
10.1007/s10114-015-5109-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group H-n . The sharp bounds for the strong type (p, p) (1 <= p <= infinity) estimates of n-dimensional Hausdorff operators on H-n are obtained. The sharp bounds for strong (p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on H-n . The weak type (p, p) (1 <= p <= infinity) estimates are also obtained. Keywords Hausdorff operator, Heisenberg group, multilinear, sharp estimate.
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页码：1703 / 1714
页数：12
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