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Hankel operators and weak factorization for Hardy-Orlicz spaces

Aline Bonami, Sandrine Grellier (2010)

Colloquium Mathematicae

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).

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