arXiv:2408.12327 Abstract | arXiv Analytics

arXiv:2408.12327 [math.FA]Abstract References Reviews Resources

Wiener-Lebesgue point property for Sobolev Functions on Metric Spaces

Published 2024-08-22Version 1

We establish a Wiener-type integral condition for first-order Sobolev functions defined on a complete, doubling metric measure space supporting a Poincar\'e inequality. It is stronger than the Lebesgue point property, except for a marginal increase in the capacity of the set of non-Lebesgue points.

Categories: math.FA

Subjects: 46E36, 46E36, 31C15, 31C40

Keywords: wiener-lebesgue point property, metric spaces, first-order sobolev functions, wiener-type integral condition, poincare inequality

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