Published Paper

Inserted: 29 sep 2024
Last Updated: 29 sep 2024

Journal: Journal of Functional Analysis
Year: 2024

Abstract:

We study the well-known asymptotic formulas for fractional Sobolev functions à la Bourgain-Brezis-Mironescu and Maz’ya-Shaposhnikova, in a geometric approach. We show that the key to these asymptotic formulas are Rademacher’s theorem and volume growth at infinity respectively. Examples fitting our framework includes Euclidean spaces, Riemannian manifolds, Alexandrov spaces, finite dimensional Banach spaces, and some ideal sub-Riemannian manifolds.

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• On the asymptotic behaviour of the fractional Sobolev seminorms- A geometric approach