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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:385

Article

Huang Jizheng^1,2 

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

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

关键词: Hermite expansions;    Lusin area integral;    Riesz transform;    Hardy space;   

DOI  :  10.1016/j.jmaa.2011.06.075

来源: Elsevier

【 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.

【 授权许可】

Free