Characterization of Clifford-valued Hardy spaces and compensated compactness

Peng, Lizhong; Zhao, Jiman

doi:10.1090/S0002-9939-03-07034-5

Characterization of Clifford-valued Hardy spaces and compensated compactness
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by Lizhong Peng and Jiman Zhao

Proc. Amer. Math. Soc. 132 (2004), 47-58

DOI: https://doi.org/10.1090/S0002-9939-03-07034-5

Published electronically: May 22, 2003

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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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