Equivalent norms for the Morrey spaces with non-doubling measures

TL;DR

This paper explores the relationship between RBMO and Morrey spaces under non-doubling measures, providing new equivalent norms without relying on the doubling condition, which is significant in harmonic analysis.

Contribution

It introduces new equivalent norms for Morrey spaces with non-doubling measures and investigates their connection to RBMO without the doubling assumption.

Findings

Established connection between RBMO and Morrey spaces under growth conditions.

Derived new types of equivalent norms for these spaces.

Extended harmonic analysis tools to non-doubling measure contexts.

Abstract

In this paper under some growth condition we investigate the connection between RBMO and the Morrey spaces. We do not assume the doubling condition which has been a key property of harmonic analysis. We also obtain another type of equivalent norms.