Carleson embeddings and pointwise multipliers between Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper half-plane

TL;DR

This paper characterizes Carleson measures with growth functions and uses this to describe continuous injections and pointwise multipliers between Hardy-Orlicz and Bergman-Orlicz spaces of the upper half-plane.

Contribution

It provides a general framework for Carleson measures with concave or convex growth functions and characterizes pointwise multipliers between Hardy-Orlicz and Bergman-Orlicz spaces.

Findings

Characterization of Carleson measures with growth functions

Description of continuous injections between spaces

Identification of pointwise multipliers

Abstract

In this article, we give a general characterization of Carleson measures involving concave or convex growth functions. We use this characterization to establish continuous injections and also to characterize the set of pointwise multipliers between Hardy-Orlicz spaces and Bergman-Orlicz spaces.