Hankel Operators on Holomorphic Hardy–Orlicz Spaces

Abstract

We characterize the symbols of Hankel operators that extend into bounded operators from the Hardy–Orlicz \({\mathcal H^{\Phi_1}(\mathbb B^n)}\) into \({\mathcal H^{\Phi_2}(\mathbb B^n)}\) in the unit ball of \({\mathbb C^n}\) , in the case where the growth functions \({\Phi_1}\) and \({\Phi_2}\) 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 \({\mathcal H^{\Phi}(\mathbb B^n)}\) , with concave growth function, in terms of products of Hardy–Orlicz functions with convex growth functions.