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This paper aims to obtain decompositions of higher dimensional L p (R n ) functions into sums of non-tangential boundary limits of the corresponding Hardy space functions on tubes for the index range 0 < p < 1. In the one-dimensional case, Deng and Qian [5] recently obtained such Hardy space decomposition result: for any function f ∈ L p (R), 0 < p < 1, there exist functions f 1 and f 2 such that f = f 1 + f 2 , where f 1 and f 2 are, respectively, the non-tangential boundary limits of some Hardy space functions in the upper-half and lower-half planes. In the present paper, we generalize the one-dimensional Hardy space decomposition result to the higher dimensions, and discuss the uniqueness issue of such decomposition.

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