Hankel Operators and Weak Factorization for Hardy-Orlicz Spaces

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).