We consider Sobolev spaces on Riemannian manifolds. A natural question to ask is whether these spaces are an algebra under the pointwise product as in the Euclidean case. We shall give sufficient conditions on the underlying Laplace-Beltrami operator to ensure such algebra properties, and describe implications for chain rules and paralinearisation formulas. Our results rely on abstract paraproducts defined via functional calculus for self-adjoint operators. This is joint work with F. Bernicot and T. Coulhon.
Paraproducts and Sobolev algebras on Riemannian manifolds
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Nom de l'orateur
Dorothée Frey
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Nantes
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