Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10140318 | Nonlinear Analysis: Theory, Methods & Applications | 2019 | 14 Pages |
Abstract
In this paper we present an interpolation approach to the fractional Sobolev spaces in Carnot groups using the K-method. This approach provides us with a different characterization of these Sobolev spaces, moreover, it provides us with the limiting behavior of the fractional Sobolev norms at the end-points. This allows us to deduce results similar to the Bourgain-Brezis-Mironescu and Maz'ya-Shaposhnikova in the case p>1
and Dávila's result in the case p=1. Also, this allows us to deduce the limiting behavior of the fractional perimeter in Carnot groups.
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Authors
Ali Maalaoui, Andrea Pinamonti,