Hankel operators and weak factorization for Hardy-Orlicz spaces

Aline Bonami, and Sandrine Grellier. "Hankel operators and weak factorization for Hardy-Orlicz spaces." Colloquium Mathematicae 118.1 (2010): 107-132. <http://eudml.org/doc/283960>.

@article{AlineBonami2010,
abstract = {We study the holomorphic Hardy-Orlicz spaces $ ^\{Φ\}(Ω)$, where Ω is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in ℂⁿ. The function Φ is in particular such that $ ¹(Ω)⊂ ^\{Φ\}(Ω)⊂ ^\{p\}(Ω)$ for some p > 0. We develop maximal characterizations, atomic and molecular decompositions. We then prove weak factorization theorems involving the space BMOA(Ω). As a consequence, we characterize those Hankel operators which are bounded from $ ^Φ(Ω)$ into ¹(Ω).},
author = {Aline Bonami, Sandrine Grellier},
journal = {Colloquium Mathematicae},
keywords = {holomorphic Hardy-Orlicz spaces; unit ball; convex domain of finite type; strictly pseudoconvex domain in ; weak factorization results; little Hankel operators; atomic decomposition; Szegő projection},
language = {eng},
number = {1},
pages = {107-132},
title = {Hankel operators and weak factorization for Hardy-Orlicz spaces},
url = {http://eudml.org/doc/283960},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Aline Bonami
AU - Sandrine Grellier
TI - Hankel operators and weak factorization for Hardy-Orlicz spaces
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 1
SP - 107
EP - 132
AB - We study the holomorphic Hardy-Orlicz spaces $ ^{Φ}(Ω)$, where Ω is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in ℂⁿ. The function Φ is in particular such that $ ¹(Ω)⊂ ^{Φ}(Ω)⊂ ^{p}(Ω)$ for some p > 0. We develop maximal characterizations, atomic and molecular decompositions. We then prove weak factorization theorems involving the space BMOA(Ω). As a consequence, we characterize those Hankel operators which are bounded from $ ^Φ(Ω)$ into ¹(Ω).
LA - eng
KW - holomorphic Hardy-Orlicz spaces; unit ball; convex domain of finite type; strictly pseudoconvex domain in ; weak factorization results; little Hankel operators; atomic decomposition; Szegő projection
UR - http://eudml.org/doc/283960
ER -