Inclusion between Bourgain-Morrey spaces and their weak types

Aria Pratama; Denny Ivanal Hakim

doi:10.62918/hjma.v3i2.35

Authors

Aria Pratama ITB
Denny Ivanal Hakim

DOI:

https://doi.org/10.62918/hjma.v3i2.35

Keywords:

Bourgain-Morrey space, Morrey space, weak Morrey space, inclusion property

Abstract

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.

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