Hankel Operators and Weak Factorization for Hardy-Orlicz Spaces

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We study the holomorphic Hardy-Orlicz spaces HΦ(Ω), where Ωis the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in Cn. The function Φis in particular such that H ¹(Ω) ⊂ HΦ(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(Omega). As a consequence, we characterize those Hankel operators which are bounded from H Φ(Ω) into H¹ (Ω).