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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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 283-342
Launched on MUSE
2001-04-01
Open Access
No
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