On the proper inclusion property of (discrete) Morrey spaces

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 $\mathit{\text{et}}\mathit{\text{al.}}$ in \cite{gunawan1, gunawan2}.