On the limiting behaviour of some nonlocal seminorms: a new phenomenon

2020/04/02 by Buseghin, Federico, Garofalo, Nicola, Tralli, Giulio · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.01303

Abstract

In this note we study the behaviour as s→ 0⁺ of some semigroup based Besov seminorms associated with a non-symmetric and hypoelliptic diffusion with a drift. Our results generalise a previous one of Maz'ya and Shaposhnikova for the classical fractional Sobolev spaces W^s,p, and they also underscore a new phenomenon caused by the presence of the drift.

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