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

Abstract: For $\mathbb B<sup>n$ the unit ball of $\mathbb C<sup>n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L<sup>\Phi_\alpha$, 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 $A_\alpha^{{\Phi_1}(\mathbb} B<sup>n)$ and $A_\alpha^{{\Phi_2}(\mathbb} B<sup>n)$ where $\Phi_1$ and $\Phi_2$ are either convex or concave growth functions.