Hankel Operators and Weak Factorization for Hardy-Orlicz Spaces

TL;DR

This paper explores Hardy-Orlicz spaces on complex domains, providing new characterizations, decompositions, and weak factorization theorems, and characterizes bounded Hankel operators between these spaces.

Contribution

It introduces maximal, atomic, and molecular characterizations of Hardy-Orlicz spaces and establishes weak factorization theorems involving BMOA, extending the understanding of Hankel operators.

Findings

Developed maximal, atomic, and molecular decompositions for Hardy-Orlicz spaces.

Proved weak factorization theorems involving BMOA.

Characterized bounded Hankel operators from Hardy-Orlicz to H^1.

Abstract

We study the holomorphic Hardy-Orlicz spaces H^\Phi(\Omega), where \Omega is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in Cn . The function \Phi is in particular such that H ^1(\Omega) \subset H^\Phi (\Omega) \subset H ^p (\Omega) for some p > 0. We develop for them maximal characterizations, atomic and molecular decompositions. We then prove weak factorization theorems involving the space BMOA(Omega). As a consequence, we characterize those Hankel operators which are bounded from H ^\Phi(\Omega) into H^1 (\Omega).