Sobolev algebra through a " carré du champ " identity

Frederic Bernicot (1) , Dorothee Frey (2)

1 Equations aux dérivées partielles
2 DIAM - Delft Institute of Applied Mathematics

We consider abstract Sobolev spaces of Bessel-type associated with an operator. In this work, we pursue the study of algebra properties of such functional spaces through the corresponding semigroup. As a follow-up of [4], we show that under the extra property of a " carré du champ identity " , this algebra property holds in a wider range than previously shown.

Domaines: Analyse classique [math.CA]

Frederic Bernicot, Dorothee Frey. Sobolev algebra through a " carré du champ " identity. Proceedings of the Edinburgh Mathematical Society, 2018, 61 (4), pp.1041-1054. ⟨hal-01406539⟩