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In this paper, the general Clifford Rn,s-valued Hardy spaces and conjugate Hardy spaces are characterized. In particular, each function in Rnvalued 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.doi:10.1090/s0002-9939-03-07034-5 fatcat:qd7plezzknajrmmrvi46yiyqxi