# Orlicz_Spaces and Orlicz_Sobolev_space

## TL;DR

This paper introduces new classes of Orlicz spaces and Orlicz Sobolev spaces by relaxing traditional definitions of Young functions and related convex functions, expanding the functional analysis framework.

## Contribution

It defines novel classes of Orlicz and Orlicz Sobolev spaces through relaxed convex function definitions, broadening the scope of these function spaces.

## Key findings

- New classes of Orlicz spaces introduced
- New classes of Orlicz Sobolev spaces defined
- Framework for generalized convex functions established

## Abstract

A new class of convex functions called functions, Young functions, strong Young functions and Orlicz functions are introduced by relaxing the definitions of functions, Young functions, strong Young functions and Orlicz functions. Then, new classes of Orlicz spaces and Orlicz Sobolev space will be defined.

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Source: https://tomesphere.com/paper/1905.06248