Duality for large Bergman-Orlicz spaces and Boundedness of Hankel Operators

Abstract

For ${\mathbb{B}}^n$ the unit ball of ${\mathbb{C}}^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L_{\alpha }^{\Phi }$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz space, and bounded Hankel operators between some Bergman-Orlicz spaces $A_{\alpha }^{{\Phi }_1}({\mathbb{B}}^n)$ and $A_{\alpha }^{{\Phi }_2}({\mathbb{B}}^n)$ where ${\Phi }_1$ and ${\Phi }_2$ are either convex or concave growth functions.