A generalization of representation theorems in Hardy-Orlicz spaces on the upper complex half-plane

TL;DR

This paper extends representation theorems in Hardy-Orlicz spaces on the upper half-plane, enabling new insights into dual spaces and classical operators within these function spaces.

Contribution

It provides Poisson and Cauchy representation theorems for Hardy-Orlicz spaces, advancing the understanding of their dual spaces and operator characterizations.

Findings

Poisson and Cauchy representation theorems established

Dual spaces of Hardy-Orlicz spaces characterized

Classical operators in Orlicz spaces analyzed

Abstract

In this paper, we give Poisson and Cauchy representation theorems in Hardy-Orlicz spaces on the upper complex half-plane. We use these theorems for the construction of dual spaces of certain Hardy-Orlicz spaces and also for the characterization of some classical operators in Orlicz spaces.