Factorization of sequences in discrete Hardy spaces

The purpose of this paper is to obtain a discrete version for the Hardy spaces H-P(Z) of the weak factorization results obtained for the real Hardy spaces H-P(R-n) by Coifman, Rochberg and Weiss for p > n/(n + 1), and by Miyachi for p <= n/(n + 1). It represents an extension, in the one-dimensional case, of the corresponding result by A. Uchiyama who obtained a factorization theorem in the general context of spaces X of homogeneous type, but with some restrictions on the measure that exclude the case of points of positive measure on X and, hence, Z. In order to obtain the factorization theorem, we first study the boundedness of some bilinear maps defined on discrete Hardy spaces.