On the proper inclusion property of (discrete) Morrey spaces

TL;DR

This paper demonstrates the proper inclusion property of Morrey spaces by constructing a simpler function that relates continuous and discrete Morrey spaces, advancing understanding of their structure.

Contribution

It introduces a new, simpler function to confirm the proper inclusion property of Morrey spaces, improving upon previous constructions.

Findings

Confirmed the proper inclusion property of Morrey spaces

Established a relation between continuous and discrete Morrey spaces

Provided a simpler construction than previous methods

Abstract

In this paper, we construct a function which confirms the proper inclusion property of Morrey spaces, by using a relation between a class of functions in Morrey spaces and discrete Morrey spaces. Our particular function is simpler than those constructed by Gunawan \textit{et al.} in \cite{gunawan1, gunawan2}.