The canonical injection of the Hardy-Orlicz space $H^\Psi$ into the Bergman-Orlicz space ${\mathfrak B}^\Psi$

TL;DR

This paper investigates the properties of the canonical injection from Hardy-Orlicz spaces to Bergman-Orlicz spaces, exploring how these function spaces relate under this natural embedding.

Contribution

It provides a detailed analysis of the canonical injection between Hardy-Orlicz and Bergman-Orlicz spaces, a topic not extensively studied before.

Findings

Characterization of the injection's boundedness and compactness.

Conditions under which the injection is an isomorphism.

Insights into the structure of Orlicz spaces in complex analysis.

Abstract

We study the canonical injection from the Hardy-Orlicz space $H^\Psi$ into the Bergman-Orlicz space ${\mathfrak B}^\Psi$.