Characterizations of parabolic reverse H\"older classes

TL;DR

This paper explores the properties of parabolic reverse H"older classes, providing new characterizations and establishing a self-improving property, with implications for parabolic weights and inequalities.

Contribution

It introduces several new characterizations of parabolic reverse H"older classes and proves a Gehring type self-improving property specific to the parabolic setting.

Findings

New characterizations of parabolic reverse H"older classes

Establishment of a Gehring type self-improving property

Insights into parabolic geometry and time lag challenges

Abstract

This paper discusses parabolic reverse H\"older inequalities and their connections to parabolic Muckenhoupt weights. The main result gives several characterizations for this class of weights. There are challenging features related to the parabolic geometry and the time lag, for example, in covering and chaining arguments. We also prove a Gehring type self-improving property for parabolic reverse H\"older inequalities.