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arXiv · 2107.05022

Characterizations of weak reverse Hölder inequalities on metric measure spaces

Juha Kinnunen·Emma-Karoliina Kurki·Carlos Mudarra
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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 $A_\infty$ 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 $A_\infty$ weights that fail to hold for weak $A_\infty$ weights.

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Juha Kinnunen, Emma-Karoliina Kurki, Carlos Mudarra. 2021-12-30. Characterizations of weak reverse Hölder inequalities on metric measure spaces. https://arxiv.org/abs/2107.05022

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