Strong A-infinity weights are A-infinity weights on metric spaces

TL;DR

This paper proves that strong A-infinity weights are equivalent to A-infinity weights in Ahlfors-regular metric spaces with Poincare inequalities, clarifying their relationships and implications.

Contribution

It establishes the equivalence of strong A-infinity weights and A-infinity weights in a broad metric space setting, extending classical results.

Findings

Strong A-infinity weights are A-infinity weights in the specified setting

Various definitions of A-infinity weights are related in this context

The proof relies on properties of Ahlfors-regular spaces and Poincare inequalities

Abstract

We prove that every strong A-infinity weight is a Muckenhoupt weight in Ahlfors-regular metric measure spaces that support a Poincare inequality. We also explore the relations between various definitions for A-infinity weights in this setting, since some of these characterizations are needed in the proof of the main result.