Non-local Gehring lemmas in spaces of homogeneous type and applications

TL;DR

This paper establishes self-improving properties for non-local reverse Hölder inequalities and extends A∞ weights in spaces of homogeneous type, with applications to elliptic, parabolic, and fractional PDEs.

Contribution

It introduces new non-local Gehring lemmas in spaces of homogeneous type, broadening the scope of regularity results for PDEs and weight classes.

Findings

Proved self-improving properties for non-local reverse Hölder inequalities.

Extended A∞ weights to non-local settings in spaces of homogeneous type.

Applicable to elliptic, parabolic, and fractional partial differential equations.

Abstract

We prove a self-improving property for reverse H{\"o}lder inequalities with non-local right hand side. We attempt to cover all the most important situations that one encounters when studying elliptic and parabolic partial differential equations as well as certain fractional equations. We also consider non-local extensions of A$\infty$ weights. We write our results in spaces of homogeneous type.