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algebra property

Proceedings of the Edinburgh Mathematical Society (1)

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Sobolev Algebras Through a ‘Carré Du Champ’ Identity
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Frédéric Bernicot, Dorothee Frey
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 61 / Issue 4 / November 2018

Published online by Cambridge University Press:

24 July 2018, pp. 1041-1054
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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.