On the limiting behaviour of some nonlocal seminorms: a new phenomenon
Abstract
In this note we study the behaviour as $s\to 0^+$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.01303
- arXiv:
- arXiv:2004.01303
- Bibcode:
- 2020arXiv200401303B
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- The paper is going to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci