Multi-Parameter Weak Bourgain-Morrey Spaces

Abstract

This paper generalizes the concept of weak Bourgain-Morrey spaces introduced by Pratama and Hakim [1]. We defi ne a new class of function spaces, termed multi-parameter weak Bourgain-Morrey spaces , , p s M q r    , which incorporate additional parameters for fi ner control over the spatial and distributional behavior of functions. We then establish the fundamental inclusion properties between these spaces. Our results extend the main fi ndings of Pratama and Hakim, demonstrating that under specifi c conditions on the parameters p,q.s,r, the chain of inclusions ,,, 2 21 , ,, 2 21 2 21 ps ps ps q r qp r q r        holds. This provides a more flexible framework for analyzing function spaces in harmonic analysis.