Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori

被引：21

作者：

Xia, Runlian ^{[1
,2
]}

Xiong, Xiao ^{[2
]}

Xu, Quanhua ^{[1
,2
,3
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Univ Franche Comte, Math Lab, F-25030 Besancon, France

[3] Inst Univ France, Paris, France

来源：

ADVANCES IN MATHEMATICS | 2016年 / 291卷

关键词：

Noncommutative L-P-spaces; Operator-valued Hardy spaces; BMO; Carleson measures; Calderon-Zygmund operators; Square functions; Characterizations; Poisson integral; Quantum tori;

D O I：

10.1016/j.aim.2015.12.023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper studies the operator-valued Hardy spaces introduced and studied by Tao Mei. Our principal result shows that the Poisson kernel in Mei's definition of these spaces can be replaced by any reasonable test function. As an application, we get a general characterization of Hardy spaces on quantum tori. The latter characterization plays a key role in our recent study of Triebel-Lizorkin spaces on quantum tori. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：183 / 227

页数：45

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