Wiener-Lebesgue point property for Sobolev Functions on Metric Spaces

2024/08/22 by Bhat, M. Ashraf, Kosuru, G. Sankara Raju
#31C15 #31C40 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46E36 #Secondary 46E36

paper · doi:10.48550/arxiv.2408.12327

Abstract

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

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