A theorem by Wolff states that weights defined on a measurable subset of Rn 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.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - Feb 2022|
|MoE publication type||A1 Journal article-refereed|
- Doubling condition
- Metric measure space
- Muckenhoupt weight