Characterizations of weak reverse Hölder inequalities on metric measure spaces

Funding Information: E.-K. Kurki has been funded by a young researcher’s grant from the Emil Aaltonen Foundation. C. Mudarra acknowledges financial support from the Academy of Finland. Publisher Copyright: © 2022, The Author(s).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.Peer reviewe