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

TL;DR

This paper characterizes the dual spaces of large Bergman-Orlicz spaces on the unit ball in complex space and investigates the boundedness of Hankel operators between these generalized spaces.

Contribution

It provides a duality characterization for large Bergman-Orlicz spaces and establishes conditions for bounded Hankel operators between them.

Findings

Dual space characterization of large Bergman-Orlicz spaces.

Boundedness criteria for Hankel operators between Bergman-Orlicz spaces.

Extension of classical results to spaces with convex or concave growth functions.

Abstract

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^\Phi_\alpha$, 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.