Sobolev algebras on lie groups and riemannian manifolds

Thierry Coulhon; Emmanuel Russ; Valérie Tardivel-Nachef

doi:10.1353/ajm.2001.0009

Sobolev algebras on lie groups and riemannian manifolds

Thierry Coulhon
, Emmanuel Russ
, Valérie Tardivel-Nachef

CY Cergy Paris Université
Aix Marseille Université

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We prove that on any connected unimodular Lie group G, the space L^P_α(G) ∩ L∞(G), where L^P_α(G) is the Sobolev space of order α > 0 associated with a sublaplacian, is an algebra under pointwise product. This generalizes results due to Strichartz (in the Euclidean case), to Bohnke (in the case of stratified groups), and others. A global version of this fact holds for groups with polynomial growth. We give similar results for Riemannian manifolds with Ricci curvature bounded from below, respectively nonnegative.

langue originale	Anglais
Pages (de - à)	283-342
Nombre de pages	60
journal	American Journal of Mathematics
Volume	123
Numéro de publication	2
Les DOIs	https://doi.org/10.1353/ajm.2001.0009
état	Publié - 1 janv. 2001
Modification externe	Oui

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10.1353/ajm.2001.0009

Contient cette citation

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title = "Sobolev algebras on lie groups and riemannian manifolds",

abstract = "We prove that on any connected unimodular Lie group G, the space LPα(G) ∩ L∞(G), where LPα(G) is the Sobolev space of order α > 0 associated with a sublaplacian, is an algebra under pointwise product. This generalizes results due to Strichartz (in the Euclidean case), to Bohnke (in the case of stratified groups), and others. A global version of this fact holds for groups with polynomial growth. We give similar results for Riemannian manifolds with Ricci curvature bounded from below, respectively nonnegative.",

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AU - Russ, Emmanuel

AU - Tardivel-Nachef, Valérie

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N2 - We prove that on any connected unimodular Lie group G, the space LPα(G) ∩ L∞(G), where LPα(G) is the Sobolev space of order α > 0 associated with a sublaplacian, is an algebra under pointwise product. This generalizes results due to Strichartz (in the Euclidean case), to Bohnke (in the case of stratified groups), and others. A global version of this fact holds for groups with polynomial growth. We give similar results for Riemannian manifolds with Ricci curvature bounded from below, respectively nonnegative.

AB - We prove that on any connected unimodular Lie group G, the space LPα(G) ∩ L∞(G), where LPα(G) is the Sobolev space of order α > 0 associated with a sublaplacian, is an algebra under pointwise product. This generalizes results due to Strichartz (in the Euclidean case), to Bohnke (in the case of stratified groups), and others. A global version of this fact holds for groups with polynomial growth. We give similar results for Riemannian manifolds with Ricci curvature bounded from below, respectively nonnegative.

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DO - 10.1353/ajm.2001.0009

M3 - Article

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SN - 0002-9327

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SP - 283

EP - 342

JO - American Journal of Mathematics

JF - American Journal of Mathematics

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Sobolev algebras on lie groups and riemannian manifolds

Résumé

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