On the extension of Muckenhoupt weights in metric spaces
Classical Analysis and ODEs
2021-10-26 v4 Metric Geometry
Abstract
A theorem by Wolff states that weights defined on a measurable subset of 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.
Keywords
Cite
@article{arxiv.2012.12857,
title = {On the extension of Muckenhoupt weights in metric spaces},
author = {Emma-Karoliina Kurki and Carlos Mudarra},
journal= {arXiv preprint arXiv:2012.12857},
year = {2021}
}
Comments
20 pages. We have rewritten part of the introduction, as well as the beginnings of Sections 3 and 4, to state our relation to an earlier result in more explicit terms