Factorization of sequences in discrete Hardy spaces

Santiago Boza. "Factorization of sequences in discrete Hardy spaces." Studia Mathematica 209.1 (2012): 53-69. <http://eudml.org/doc/285527>.

@article{SantiagoBoza2012,
abstract = {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 $H^\{p\}(ℝⁿ)$ 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.},
author = {Santiago Boza},
journal = {Studia Mathematica},
keywords = {discrete Hardy space; discrete Hilbert transform; factorization; atom},
language = {eng},
number = {1},
pages = {53-69},
title = {Factorization of sequences in discrete Hardy spaces},
url = {http://eudml.org/doc/285527},
volume = {209},
year = {2012},
}

TY - JOUR
AU - Santiago Boza
TI - Factorization of sequences in discrete Hardy spaces
JO - Studia Mathematica
PY - 2012
VL - 209
IS - 1
SP - 53
EP - 69
AB - 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 $H^{p}(ℝⁿ)$ 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.
LA - eng
KW - discrete Hardy space; discrete Hilbert transform; factorization; atom
UR - http://eudml.org/doc/285527
ER -