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Abstract

The purpose of this paper is to obtain a discrete version for the Hardy spaces $H^p(\mathbb{Z})$ of the weak factorization results obtained for the real Hardy spaces $H^p(\mathbb{R}^n)$ by Coifman, Rochberg and Weiss for $p>n/(n+1)$, and by Miyachi for $p\leq n/(n+1)$. 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, $\mathbb{Z}$. In order to obtain the factorization theorem, we first study the boundedness of some bilinear maps defined on discrete Hardy spaces.