×

zbMATH — the first resource for mathematics

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.
PDF BibTeX XML Cite
Full Text: DOI Link