INCLUSION IN THE BOURGAIN-MORREY SPACE AND ITS GENERALIZATION - Pratama, Aria
This research explores inclusion in several variants of Bourgain-Morrey space, namely Bourgain-Morrey space, mixed Bourgain-Morrey space, and weak Bourgain-Morrey space. The Bourgain-Morrey space is a generalization of the classical Morrey space that is widely used in harmonic analysis and function theory. First, the properties and inclusions in the Bourgain-Morrey space are discussed again. Apart from that, the conditions for a Bourgain-Morrey space to have non-trivial elements are also discussed. Next, adapting a definition of mixed Morrey spaces, the definition of mixed Bourgain-Morrey spaces is introduced and its inclusion properties are investigated. Finally, adapting the definition of a weak Morrey space, the definition of a weak Bourgain-Morrey space is also introduced and its inclusion properties are examined. .