THE STRUCTURE OF DISCRETE MORREY SPACES AND THEIR INTERMEDIATE SPACES - Yudatama, Rizma
In this thesis we study the structure of discrete Morrey spaces, the relation between discrete Morrey spaces and Morrey spaces, and intermediate spaces in discrete Morrey spaces. The necessary and sufficient conditions for a discrete Morrey space to be a subspace of another discrete Morrey space have been studied by Gunawan et al. (2018) and also Haroske and Skrzypczak (2020). In addition to the relation between two discrete Morrey spaces, the relation between discrete Morrey spaces and Morrey spaces has been studied. Kikianty and Schwanke (2019) found that discrete Morrey spaces can be viewed as closed subspaces of Morrey spaces. In this thesis, the necessary and sufficient conditions for a discrete Morrey space to be a subspace of another discrete Morrey space and the relation between discrete Morrey spaces and Morrey spaces will be studied and re-proved with alternative evidence. As a continuation of inclusion research on discrete Morrey spaces, the intermediate space in the family of discrete Morrey spaces is investigated. The result is that apart from the trivial case, namely when there is an inclusion relation between two discrete Morrey spaces, the only members of the intermediate space family of a Banach pair of two discrete Morrey spaces that are in the form of a discrete Morrey space are the two discrete Morrey spaces themselves.