Sobolev algebras on Lie groups and Riemannian manifolds (Q2731069)
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scientific article; zbMATH DE number 1625517
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sobolev algebras on Lie groups and Riemannian manifolds |
scientific article; zbMATH DE number 1625517 |
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Sobolev algebras on Lie groups and Riemannian manifolds (English)
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29 July 2001
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Sobolev algebras
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Sobolev space
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unimodular Lie group
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Riemannian manifolds
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0.9556952
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0.9495515
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0.93161166
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0.9290736
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0.92354774
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0.9231069
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0.92124254
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0.92085713
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We denote by \(L^p_\alpha (G)\) the Sobolev space of order \(\alpha\) associated with a sublaplacian on a connected unimodular Lie group. In this paper the authors prove that the space \(L^p_\alpha (G)\cap L^\infty (G)\) is an algebra under pointwise product. A global version of this fact holds for groups with polynomial growth. They give also similar results for Riemannian manifolds with Ricci curvature bounded from below, respectively nonnegative.
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