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Sobolev algebras on Lie groups and Riemannian manifolds. (English) Zbl 0990.43003
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.

##### MSC:
 43A15 $$L^p$$-spaces and other function spaces on groups, semigroups, etc.
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