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Sobolev Algebras Through a ‘Carré Du Champ’ Identity

Published online by Cambridge University Press:  24 July 2018

Frédéric Bernicot
Affiliation:
CNRS – Université de Nantes, Laboratoire Jean Leray, 2 rue de la Houssinière, 44322 Nantes cedex 3, France ([email protected])
Dorothee Frey
Affiliation:
Delft Institute of Applied Mathematics, Delft University of Technology, PO Box 5031, 2600 GA Delft, The Netherlands ([email protected])

Abstract

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 to our previous work, we show that by making use of the property of a ‘carré du champ’ identity, this algebra property holds in a wider range than previously shown.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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