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Sobolev algebras on Lie groups and Riemannian manifolds
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 123, Number 2, April 2001
- pp. 283-342
- 10.1353/ajm.2001.0009
- Article
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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.