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Sobolev Algebras Through a ‘Carré Du Champ’ Identity

Part of: Abstract harmonic analysis Linear function spaces and their duals Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  24 July 2018

Frédéric Bernicot  and
Dorothee Frey
Frédéric Bernicot
Affiliation:
CNRS – Université de Nantes, Laboratoire Jean Leray, 2 rue de la Houssinière, 44322 Nantes cedex 3, France (frederic.bernicot@univ-nantes.fr)
Dorothee Frey
Affiliation:
Delft Institute of Applied Mathematics, Delft University of Technology, PO Box 5031, 2600 GA Delft, The Netherlands (d.frey@tudelft.nl)
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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.

Keywords

Sobolev spacealgebra propertyheat semigroup

MSC classification

Primary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Secondary: 43A85: Analysis on homogeneous spaces 47D06: One-parameter semigroups and linear evolution equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 1041 - 1054
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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