Characterizations of weak reverse Hölder inequalities on metric measure spaces

2021/07/11 by Kinnunen, Juha, Kurki, Emma-Karoliina, Mudarra, Carlos · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.05022

Abstract

We present ten different characterizations of functions satisfying a weak reverse Hölder inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak A_∞ weights, which is a generalization of Muckenhoupt weights that allows for nondoubling weights. Although our main results are modeled after conditions that hold true for Muckenhoupt weights, we also discuss two conditions for Muckenhoupt A_∞ weights that fail to hold for weak A_∞ weights.

Cited by

• A note on some reverse inequalities for scalar Birkhoff weak integrable functions

Related

• Limiting conditions of Muckenhoupt and reverse Hölder classes on metric measure spaces
• Weak Gurov-Reshetnyak class in metric measure spaces
• Reverse Hölder Property for strong weights and general measures
• On the extension of Muckenhoupt weights in metric spaces
• Reverse Holder inequalities revisited: Interpolation, Extrapolation, Indices and Doubling