Inclusion between Bourgain-Morrey spaces and their weak types - Pratama, Aria; Ivanal Hakim, Denny (KOMUNITAS Analisis Matematika INDONESIA, 2025)
This paper aims to explore the embedding relation between Bourgain-Morrey spaces and weak Bourgain-Morrey spaces. Bourgain-Morrey Spaces are important function spaces in harmonic analysis. In this article, we introduce weak Bourgain-Morrey spaces as certain generalization of weak Morrey spaces. We investigate the necessary and sufficient conditions for functions in weak Bourgain-Morrey spaces to also be elements in Bourgain-Morrey spaces, and vice versa. Our result are inclusion between weak Bourgain-Morrey spaces and inclusion of weak Bourgain- Morrey spaces into a certain Bourgain-Morrey spaces. These result generelize the inclusion result in Morrey spaces, weak Morrey spaces, and Bourgain- Morrey spaces.