Modular convergence in $H$-Orlicz spaces of Banach valued functions

TL;DR

This paper develops the theory of $H$-Orlicz spaces generated by generalized Young functions, focusing on modular and norm convergence for Banach-valued functions and exploring their relationships.

Contribution

It introduces the theory of $H$-Orlicz spaces with generalized Young functions and analyzes modular and norm convergence for vector-valued functions.

Findings

Established the framework for $H$-Orlicz spaces with generalized Young functions.

Analyzed the relationship between modular and norm convergence in these spaces.

Extended convergence concepts to Banach-valued functions.

Abstract

In this article we develop the theory of $H$-Orlicz space generated by generalised Young function. Modular convergence of $H$-Orlicz space for the case of vector-valued functions and norm convergence in $\mcH^\theta(X, \bar{\mu})$ where $X$ is any Banach space are discussed. Relationships of modular convergence and norm convergence of $H$-Orlicz spaces are discussed.