Characterization of Clifford-valued Hardy spaces and compensated compactness |
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| Authors: | Lizhong Peng Jiman Zhao |
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| Affiliation: | LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, People's Republic of China ; 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 |
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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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| Keywords: | Clifford algebra Cauchy-Riemann operator Hardy space compensated compactness paracommutator |
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