BMO spaces for nondoubling metric measure spaces

TL;DR

This paper explores the structure and relationships of BMO^p spaces in general metric measure spaces, providing a characterization theorem, examples, and insights into the John--Nirenberg inequality.

Contribution

It introduces a comprehensive characterization theorem for BMO^p spaces in nondoubling metric measure spaces, expanding understanding of their interrelations.

Findings

Characterization theorem for BMO^p spaces

Examples illustrating different relations between BMO^p spaces

Results related to the John--Nirenberg inequality

Abstract

In this article we study the family of $BMO^p$ spaces, $p \geq 1$, in the general context of metric measure spaces. We give a characterization theorem that allows to describe all possible relations between these spaces considered as sets of functions. Examples illustrating the obtained cases and some additional results related to the John--Nirenberg inequality are also included.