Sobolev Algebras on Lie Groups and Riemannian Manifolds

We prove that on any connected unimodular Lie group G, the space$L_{\alpha}^{p}(G)\cap L^{\infty}(G)$, where$L_{\alpha}^{p}(G)$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 ca...

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Veröffentlicht in:	American journal of mathematics 2001-04, Vol.123 (2), p.283-342
Hauptverfasser:	Coulhon, Thierry, Russ, Emmanuel, Tardivel-Nachef, Valérie
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Curvature Lie groups Mathematical inequalities Mathematical theorems Mathematics Polynomials Riemann manifold Semigroups Sobolev spaces
Online-Zugang:	Volltext
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