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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Various characterizations of product Hardy space


Authors: Ji Li, Liang Song and Chaoqiang Tan
Journal: Proc. Amer. Math. Soc. 139 (2011), 4385-4400
MSC (2010): Primary 42B30, 42B35; Secondary 42B25, 46E40
Published electronically: April 22, 2011
MathSciNet review: 2823084
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Abstract: This article deals with the characterizations of Hardy space $ H^1$ on $ \mathbb{R}^n\times\mathbb{R}^m$ using different norms on distinct variables. This result can be applied to the boundedness of certain operators on $ H^1(\mathbb{R}^n\times\mathbb{R}^m)$.


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Additional Information

Ji Li
Affiliation: Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China
Email: liji6@mail.sysu.edu.cn

Liang Song
Affiliation: Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China
Email: songl@mail.sysu.edu.cn

Chaoqiang Tan
Affiliation: Department of Mathematics, Shantou University, Shantou, 515063, People’s Republic of China
Email: cqtan@stu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10852-9
PII: S 0002-9939(2011)10852-9
Keywords: Multiparameter harmonic analysis, Hardy space
Received by editor(s): July 10, 2010
Received by editor(s) in revised form: July 27, 2010, and October 20, 2010
Published electronically: April 22, 2011
Additional Notes: The first author is supported by NNSF of China (11001275).
The second author is supported by NNSF of China (11001276) and is the corresponding author.
The third author is supported by FDYT of Guangdong (LYM08059).
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2011 American Mathematical Society