Composition operators on Bergman-Orlicz spaces on the ball

TL;DR

This paper establishes embedding theorems for weighted Bergman-Orlicz spaces on the ball and investigates the boundedness of composition operators, revealing spaces where all such operators are bounded, unlike classical spaces.

Contribution

It provides new embedding theorems for weighted Bergman-Orlicz spaces and demonstrates the existence of spaces with universally bounded composition operators.

Findings

Existence of weighted Bergman-Orlicz spaces with all composition operators bounded

New embedding theorems for these spaces on the ball

Identification of spaces different from $H^{inity}$ with bounded composition operators

Abstract

We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted Bergman-Orlicz spaces, different from $H^{\infinity}$, on which every composition operator is bounded.