This paper aims to obtain decompositions of higher dimensional L(R) 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 recently obtained such a Hardy space decomposition result: for any function f ∈ L(R), 0 < p < 1, there exist functions f and f such that f = f + f, where f and f 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.