Carleson embeddings for Hardy-Orlicz and Bergman-Orlicz spaces of the upper-half plane

TL;DR

This paper characterizes off-diagonal Carleson embeddings for Hardy-Orlicz and Bergman-Orlicz spaces on the upper-half plane, leading to new embedding relations and pointwise multiplier results.

Contribution

It provides a comprehensive characterization of off-diagonal Carleson embeddings for Hardy-Orlicz and Bergman-Orlicz spaces, which was previously unexplored.

Findings

Characterization of off-diagonal Carleson embeddings

New embedding relations between Hardy-Orlicz and Bergman-Orlicz spaces

Identification of pointwise multipliers between these spaces

Abstract

In this paper we characterize off-diagonal Carleson embeddings for both Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper-half plane. We use these results to obtain embedding relations and pointwise multipliers between these spaces.