Hankel operators and weak factorization for Hardy–Orlicz spaces

Abstract

We study the holomorphic Hardy-Orlicz spaces H^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 H ^1(Ω) ⊂ H^Φ (Ω) ⊂ H ^p (Ω) for some p > 0. We develop for them 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 H ^Φ(Ω) into H^1 (Ω).