-CARLESON MEASURES AND MULTIPLIERS BETWEEN BERGMAN–ORLICZ SPACES OF THE UNIT BALL OF

Abstract

We define the notion of $\unicode[STIX]{x1D6F7}$-Carleson measures, where $\unicode[STIX]{x1D6F7}$ is either a concave growth function or a convex growth function, and provide an equivalent definition. We then characterize $\unicode[STIX]{x1D6F7}$-Carleson measures for Bergman–Orlicz spaces and use them to characterize multipliers between Bergman–Orlicz spaces.