Factorization of sequences in discrete Hardy spaces

Santiago Boza¹

¹ Department of Applied Mathematics IV EPSEVG Polytechnical University of Catalonia E-08880 Vilanova i Geltrú, Spain

Studia Mathematica, Tome 209 (2012) no. 1, pp. 53-69

Résumé

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.

Détail

DOI : 10.4064/sm209-1-5

Keywords: purpose paper obtain discrete version hardy spaces mathbb weak factorization results obtained real hardy spaces mathbb coifman rochberg weiss miyachi leq represents extension one dimensional corresponding result uchiyama who obtained factorization theorem general context spaces homogeneous type restrictions measure exclude points positive measure hence mathbb order obtain factorization theorem first study boundedness bilinear maps defined discrete hardy spaces