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

 

Characterization of Clifford-valued Hardy spaces and compensated compactness


Authors: Lizhong Peng and Jiman Zhao
Journal: Proc. Amer. Math. Soc. 132 (2004), 47-58
MSC (2000): Primary 15A66, 42B30, 46J15, 47B35
Published electronically: May 22, 2003
MathSciNet review: 2021247
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Abstract: In this paper, the general Clifford $R_{n,s}$-valued Hardy spaces and conjugate Hardy spaces are characterized. In particular, each function in $R_n$-valued Hardy space can be determined by half of its function components through Riesz transform, and the explicit determining formulas are given. The products of two functions in the Hardy space give six kinds of compensated quantities, which correspond to six paracommutators, and their boundedness, compactness and Schatten-von Neumann properties are given.


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Additional Information

Lizhong Peng
Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
Email: lzpeng@pku.edu.cn

Jiman Zhao
Affiliation: Department of Mathematics, Beijing Normal University, Beijing, 100875, People’s Republic of China – and – Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, People’s Republic of China
Email: jmz70@sina.com

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07034-5
PII: S 0002-9939(03)07034-5
Keywords: Clifford algebra, Cauchy-Riemann operator, Hardy space, compensated compactness, paracommutator
Received by editor(s): November 15, 2001
Received by editor(s) in revised form: September 4, 2002
Published electronically: May 22, 2003
Additional Notes: Research supported by NNSF of China Nos. 90104004 and 69735020 and 973 project of China G1999075105
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society