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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-5,
author = {Santiago Boza},
title = {Factorization of sequences in discrete Hardy spaces},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {53-69},
zbl = {1256.42033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-5}
}
Santiago Boza. Factorization of sequences in discrete Hardy spaces. Studia Mathematica, Tome 209 (2012) pp. 53-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-5/