Factorization of sequences in discrete Hardy spaces
Tom 209 / 2012
Streszczenie
The purpose of this paper is to obtain a discrete version for the Hardy spaces 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.