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

共 50 条

[21] Operator-Valued Triebel–Lizorkin Spaces
Runlian Xia
Xiao Xiong
Integral Equations and Operator Theory, 2018, 90
[22] OPERATOR-VALUED DYADIC BMO SPACES
Blasco, Oscar
Pott, Sandra
JOURNAL OF OPERATOR THEORY, 2010, 63 (02) : 333 - 347
[23] OPERATOR-VALUED DYADIC HARMONIC ANALYSIS BEYOND DOUBLING MEASURES
Conde-Alonso, Jose M.
Daniel Lopez-Sanchez, Luis
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (09) : 3869 - 3885
[24] HARMONIC-ANALYSIS OF COSINE AND EXPONENTIAL OPERATOR-VALUED FUNCTIONS
BASKAKOV, AG
MATHEMATICS OF THE USSR-SBORNIK, 1984, 124 (1-2): : 63 - 90
[25] APPLICATIONS OF KATO'S INEQUALITY TO OPERATOR-VALUED INTEGRALS ON HILBERT SPACES
Dragomir, S. S.
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2013, 6 (04)
[26] Finite rank harmonic operator-valued functions
Smithies, L
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 336 (1-3) : 15 - 20
[27] Dilations for operator-valued quantum measures
Han, Deguang
Hu, Qianfeng
Larson, David R.
Liu, Rui
ADVANCES IN MATHEMATICS, 2024, 438
[28] Operator valued hardy spaces - Introduction
Mei, Tao
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 188 (881) : 1 - +
[29] DECOMPOSITIONS OF OPERATOR-VALUED FUNCTIONS IN HILBERT SPACES
SZYMANSKI, W
STUDIA MATHEMATICA, 1974, 50 (03) : 265 - 280
[30] On operator-valued cosine sequences on UMD spaces
Chojnacki, Wojciech
STUDIA MATHEMATICA, 2010, 199 (03) : 267 - 278

← 1 2 3 4 5 →