On the extension of Muckenhoupt weights in metric spaces
Abstract
A theorem by Wolff states that weights defined on a measurable subset of $\mathbb{R}^n$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.12857
- arXiv:
- arXiv:2012.12857
- Bibcode:
- 2020arXiv201212857K
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- Mathematics - Metric Geometry
- E-Print:
- 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