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.
On the limiting behaviour of some nonlocal seminorms: a new phenomenon
Garofalo N.;Tralli G.
2022
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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