On Musielak N-functions

TL;DR

This paper introduces Musielak N-functions and Musielak-Orlicz spaces, exploring their properties, calculus, and relationships using measure theory, thus expanding the theoretical framework of these generalized function spaces.

Contribution

It defines Musielak N-functions and Musielak-Orlicz spaces, analyzing their properties and relationships with measure theory, which is a novel extension in the field.

Findings

Established properties of Musielak N-functions

Analyzed calculus and approximation within Musielak-Orlicz spaces

Explored relationships between Musielak N-functions and Musielak-Orlicz functions

Abstract

In this paper, the concept of Musielak N-functions and Musielak-Orlicz spaces generated by them well be introduced. Facts and results of the measure theory will be applied to consider properties, calculus and basic approximation of Musielak N-functions and their Musielak-Orlicz spaces. Finally, the relationship between Musielak N-functions and Musielak-Orlicz functions and thier Musielak-Orlicz spaces will be considered using facts and results of the measure theory too