On the extension of Muckenhoupt weights in metric spaces. (February 2022) - Kurki, Emma-Karoliina; Mudarra, Carlos
Abstract: A theorem by Wolff states that weights defined on a measurable subset of R n and satisfying a Muckenhoupt-type condition can be extended into the whole space as Muckenhoupt weights of the same class. We give a complete and self-contained proof of this theorem generalized into metric measure spaces supporting a doubling measure. Related to the extension problem, we also show estimates for Muckenhoupt weights on Whitney chains in the metric setting.