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On the extension of Muckenhoupt weights in metric spaces
2022
Nonlinear Analysis
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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 selfcontained 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.
doi:10.1016/j.na.2021.112671
fatcat:uxdnl4os5bf7neqh2eabfn5xyi