John-Nirenberg lemmas for a doubling measure

TL;DR

This paper extends the John-Nirenberg inequality to BMO functions in doubling metric measure spaces, introducing a new Calderon-Zygmund decomposition adapted to these spaces.

Contribution

It provides a novel Calderon-Zygmund decomposition for metric spaces and establishes a version of the John-Nirenberg inequality in this setting.

Findings

Established a new Calderon-Zygmund decomposition for doubling metric spaces

Proved a John-Nirenberg inequality for BMO functions in these spaces

Extended classical harmonic analysis results to a broader metric space context

Abstract

We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.