Calculus of Variations and Geometric Measure Theory
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A. Maalaoui - A. Pinamonti

Interpolations and Fractional Sobolev Spaces in Carnot Groups

created by pinamonti on 09 Aug 2018

[BibTeX]

Accepted Paper

Inserted: 9 aug 2018
Last Updated: 9 aug 2018

Journal: Nonlinear Analysis
Year: 2018

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 D\'{a}vila'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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