# A Note on Inclusions of Discrete Morrey Spaces

## TL;DR

This paper investigates inclusion relations among discrete Morrey spaces, providing necessary conditions, generalizations, and properness of these relations, along with connections to classical Morrey spaces and their weak type variants.

## Contribution

It introduces new necessary conditions for inclusion, generalizes known properties, and explores the properness and connections of these relations in discrete Morrey spaces.

## Key findings

- Established necessary inclusion conditions.
- Proved a generalization of p-summable sequence spaces.
- Showed all inclusion relations are proper.

## Abstract

We give a necessary condition for inclusion relations between discrete Morrey spaces which can be seen as a complement of the results in \cite{GKS,HS2}. We also prove another inclusion property of discrete Morrey spaces which can be viewed as a generalization of the inclusion property of the spaces of $p$-summable sequences. Analogous results for weak type discrete Morrey spaces is also presented. In addition, we show that each of these inclusion relations is proper. Some connections between inclusion properties of discrete Morrey spaces and those of Morrey spaces are also discussed.