Asymptotical stability of Muckenhoupt weights through Gurov-Reshetnyak classes
Asymptotical stability of Muckenhoupt weights through Gurov-Reshetnyak classes
We show that weights in the Gurov-Reshetnyak class $GR_\varepsilon (\mu )$ satisfy a weak reverse Hölder inequality with an explicit and asymptotically sharp bound for the exponent, thus extending classical results from the Euclidean setting to doubling metric measure spaces. As an application, we study asymptotical behaviour of embeddings between …