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Characterization of Clifford-valued Hardy spaces and compensated compactness
Author(s):
Lizhong
Peng;
Jiman
Zhao
Journal:
Proc. Amer. Math. Soc.
132
(2004),
47-58.
MSC (2000):
Primary 15A66, 42B30, 46J15, 47B35
Posted:
May 22, 2003
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Abstract:
In this paper, the general Clifford  -valued Hardy spaces and conjugate Hardy spaces are characterized. In particular, each function in  -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:
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
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
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