Henstock-Orlicz space and its dense space

TL;DR

This paper introduces the Henstock-Orlicz space for non-absolute integrable functions and proves that smooth functions are dense in this space, unlike in classical Orlicz spaces.

Contribution

It establishes the density of smooth functions in Henstock-Orlicz space, a property not present in classical Orlicz spaces, expanding the understanding of function space structures.

Findings

C_{0}^{ abla} is dense in Henstock-Orlicz space

Density property differs from classical Orlicz space

Provides new insights into non-absolute integrable functions

Abstract

The motivation of the article is to introduce Henstock-Orlicz space with non-absolute integrable functions. We prove $ C_{0}^{\infty} $ is dense in the Henstock-Orlicz space, which is not dense in the classical Orlicz space.