Dimension free properties of strong Muckenhoupt and Reverse H\"older weights for Radon measures

TL;DR

This paper establishes dimension-free self-improvement properties of strong Muckenhoupt and Reverse H"older weights for Radon measures using a Bellman function approach, extending classical results beyond Lebesgue measure.

Contribution

It introduces a novel Bellman function method that achieves dimension-independent results for a broad class of measures, generalizing previous work limited to Lebesgue measure.

Findings

Dimension-free self-improvement properties proved

Bellman function technique applied to Radon measures

Results extend classical weight theory to general measures

Abstract

In this paper we prove self-improvement properties of strong Muckenhoupt and Reverse H\"older weights with respect to a general Radon measure on $\mathbb{R}^n$. We derive our result via a Bellman function argument. An important feature of our proof is that it uses only the Bellman function for the one-dimensional problem for Lebesgue measure; with this function in hand, we derive dimension free results for general measures and dimensions.