On Orlicz Theory

TL;DR

This paper introduces new concepts and generalizations of Orlicz spaces and related function spaces, based on convex analysis, and explores their properties and operator effects.

Contribution

It proposes relaxed definitions of Orlicz-related functions and develops a broad framework of associated function spaces and their properties.

Findings

Defined new classes of Orlicz and Young functions

Established properties of generalized Orlicz spaces

Analyzed operator effects on these spaces

Abstract

In this paper, based on concepts of convex sets and convex functions, we introduce new concepts of functions, Young functions, strong Young functions and Orlicz functions by relaxing definitions of functions, Young functions, strong Young functions, Orlicz functions respectively. We also give concepts of Orlicz spaces, weak Orlicz spaces, Orlicz Sobolev spaces, weak Orlicz Sobolev spaces, Orlicz Morrey spaces and weak Orlicz Morrey spaces, Orlicz Lorentz spaces and weak Orlicz Lorentz spaces. In addition, we consider the implicit properties based on the effect of an operator on the functions and the spaces