Hankel operators on holomorphic Hardy-Orlicz spaces

Abstract

We characterize the symbols of Hankel operators that ex- tend into bounded operators from the Hardy-Orlicz $H^{Φ_1} (\mathbb B^n)$ into $H^{Φ_2} (\mathbb B^n)$ in the unit ball of Cn, in the case where the growth functions $?Φ_1$ and $Φ_2$ are either concave or convex. The case where the growth functions are both concave has been studied by Bonami and Sehba. We also obtain several weak factorization theorems for functions in $H^Φ(\mathbb B^n)$, with concave growth function, in terms of products of Hardy-Orlicz functions with convex growth functions.