The boundedness of Riesz transforms for Hermite expansions on the Hardy spaces

被引：10

作者：

Huang Jizheng ^{[1
,2
]}

机构：

[1] N China Univ Technol, Coll Sci, Beijing 100144, Peoples R China

[2] Cent Univ Finance & Econ, CEMA, Beijing 100081, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 385卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Hermite expansions; Lusin area integral; Riesz transform; Hardy space; REVERSE HOLDER INEQUALITY; SCHRODINGER-OPERATORS; POTENTIALS;

D O I：

10.1016/j.jmaa.2011.06.075

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let L = -Delta + [x](2) be a Hermite operator, where Delta is the Laplacian on R(d). In this paper, we first characterize the Hardy spaces H(L)(1)(Rd) associated with L by a new version of area integral. Then, we use it to prove the boundedness of Riesz transforms R(j)(L), j = 1.2.... for L on H(L)(1)(R(d)). Moreover, we characterize the Hardy space H(L)(1)(R(d)) by R(j)(L) This gives a negative answer to a question asked by Thangavelu. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：559 / 571

页数：13

共 50 条

[1] Endpoint boundedness of Riesz transforms on Hardy spaces associated with operators
Cao, Jun
Yang, Dachun
Yang, Sibei
[J]. REVISTA MATEMATICA COMPLUTENSE, 2013, 26 (01): : 99 - 114
[2] Endpoint boundedness of Riesz transforms on Hardy spaces associated with operators
Jun Cao
Dachun Yang
Sibei Yang
[J]. Revista Matemática Complutense, 2013, 26 : 99 - 114
[3] Riesz transforms for Dunkl Hermite expansions
Amri, Bechir
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 423 (01) : 646 - 659
[4] Boundedness of Generalized Riesz Transforms on Orlicz–Hardy Spaces Associated to Operators
Jun Cao
Der-Chen Chang
Dachun Yang
Sibei Yang
[J]. Integral Equations and Operator Theory, 2013, 76 : 225 - 283
[5] Boundedness of Generalized Riesz Transforms on Orlicz-Hardy Spaces Associated to Operators
Cao, Jun
Chang, Der-Chen
Yang, Dachun
Yang, Sibei
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2013, 76 (02) : 225 - 283
[6] Chaotic behavior of the Riesz transforms for Hermite expansions
Bermudez, Teresa
Bonilla, Antonio
Torrea, Jose L.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 337 (01) : 702 - 711
[7] Higher order Riesz transforms for Hermite expansions
Huang, Jizheng
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
[8] Higher order Riesz transforms for Hermite expansions
Jizheng Huang
[J]. Journal of Inequalities and Applications, 2017
[9] Riesz transforms and conjugacy for Laguerre function expansions of Hermite type
Nowak, Adam
Stempak, Krzysztof
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 244 (02) : 399 - 443
[10] Poisson integrals and Riesz transforms for Hermite function expansions with weights
Stempak, K
Torrea, JL
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 202 (02) : 443 - 472

← 1 2 3 4 5 →