The local sharp maximal function and BMO on locally homogeneous spaces

TL;DR

This paper establishes local versions of key inequalities for the sharp maximal function and BMO functions within locally homogeneous spaces, extending classical harmonic analysis results to a broader geometric setting.

Contribution

It introduces local Fefferman-Stein and John-Nirenberg inequalities in the framework of locally homogeneous spaces, generalizing existing results to new geometric contexts.

Findings

Proves a local Fefferman-Stein inequality for the sharp maximal function.

Establishes a local John-Nirenberg inequality for locally BMO functions.

Extends classical harmonic analysis inequalities to locally homogeneous spaces.

Abstract

We prove a local version of Fefferman-Stein inequality for the local sharp maximal function, and a local version of John-Nirenberg inequality for locally BMO functions, in the framework of locally homogeneous spaces, in the sense of Bramanti-Zhu [Manuscripta Math. 138 (2012), no. 3-4, 477-528].