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´avila’s result in the case p = 1. Also, this allows us to deduce the limiting behavior of the fractional perimeter in Carnot groups.

Interpolations and Fractional Sobolev Spaces in Carnot Groups / Pinamonti, Andrea; Maalaoui, Ali. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 179:(2019), pp. 91-104. [10.1016/j.na.2018.08.005]

Interpolations and Fractional Sobolev Spaces in Carnot Groups

Andrea Pinamonti;
2019

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´avila’s result in the case p = 1. Also, this allows us to deduce the limiting behavior of the fractional perimeter in Carnot groups.
Pinamonti, Andrea; Maalaoui, Ali
Interpolations and Fractional Sobolev Spaces in Carnot Groups / Pinamonti, Andrea; Maalaoui, Ali. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 179:(2019), pp. 91-104. [10.1016/j.na.2018.08.005]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/212415
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