# On Inclusion Properties of Two Versions of Orlicz-Morrey Spaces

## TL;DR

This paper investigates the inclusion relations between two versions of Orlicz-Morrey spaces on , providing comparisons and extending results to their weak variants, with key insights from characteristic function norms.

## Contribution

It offers a detailed comparison of the inclusion properties of two definitions of Orlicz-Morrey spaces and extends the analysis to weak spaces, clarifying their relationships.

## Key findings

- Inclusion criteria for the two versions are established.
- Norms of characteristic functions of balls are crucial for the analysis.
- Results are extended to weak Orlicz-Morrey spaces.

## Abstract

There are two versions of Orlicz-Morrey spaces (on $\mathbb{R}^n$), defined by Nakai in 2004 and by Sawano, Sugano, and Tanaka in 2012. In this paper we discuss the inclusion properties of these two spaces and compare the results. Computing the norms of the characteristic functions of balls in $\mathbb{R}^n$ is one of the keys to our results. Similar results for weak Orlicz-Morrey spaces of both versions are also obtained.