$\Phi$-Carleson measures and multipliers between Bergman-Orlicz spaces of the unit ball of $\mathbb {C}^n$

Abstract

We define the notion of $\Phi$-Carleson measures where $\Phi$ is either a concave growth function or a convex growth function and provide an equivalent definition. We then characterize $\Phi$-Carleson measures for Bergman-Orlicz spaces, and apply them to characterize multipliers between Bergman-Orlicz spaces.