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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Characterization of Clifford-valued Hardy spaces and compensated compactness
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by Lizhong Peng and Jiman Zhao PDF
Proc. Amer. Math. Soc. 132 (2004), 47-58 Request permission


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:
  • 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:
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 47-58
  • MSC (2000): Primary 15A66, 42B30, 46J15, 47B35
  • DOI:
  • MathSciNet review: 2021247