A Dyadic Gehring Inequality in Spaces of Homogeneous Type and Applications

TL;DR

This paper extends Gehring's self-improvement theorem for reverse Hölder weights to dyadic cubes in spaces of homogeneous type, exploring its implications and applications.

Contribution

It introduces a dyadic version of Gehring's inequality applicable to spaces of homogeneous type, broadening the scope of previous results.

Findings

Established a dyadic Gehring inequality in spaces of homogeneous type.

Derived new consequences and applications from the inequality.

Extended classical results to more general metric measure spaces.

Abstract

We state a version of Gehring's self improvement Theorem for reverse \Holder weights which is valid for dyadic cubes over spaces of homogeneous type and explore some of the consequences and applications.