Sobolev Algebras Through a 'Carré du Champ' Identity

Frédéric Bernicot, Dorothee Frey

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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.

Original languageEnglish
Pages (from-to)1041-1054
Number of pages14
JournalProceedings of the Edinburgh Mathematical Society
Volume61
Issue number4
DOIs
Publication statusPublished - 2018

Keywords

  • algebra property
  • heat semigroup
  • Sobolev space

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