$\mathit{BMO}$ spaces for nondoubling metric measure spaces

Abstract

In this article we study the family of $\mathit{BMO}^p$ 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.