# A Note on Inclusion Properties of Weighted Orlicz Spaces

## TL;DR

This paper establishes precise conditions for when one weighted Orlicz space is included in another, improving upon previous results by utilizing characteristic function norms of Euclidean balls.

## Contribution

It provides necessary and sufficient conditions for inclusion relations between weighted Orlicz spaces, extending Osan extcirlioul's 2014 findings.

## Key findings

- Derived new inclusion criteria for weighted Orlicz spaces.
- Utilized characteristic function norms of Euclidean balls in proofs.
- Extended previous inclusion results with complete conditions.

## Abstract

In this paper we present sufficient and necessary conditions for inclusion relation between two weighted Orlicz spaces which complete the Osan\c{c}liol result in 2014. One of the keys to prove our results is to use the norm of the characteristic functions of the balls in $\mathbb{R}^n$.