Document Zbl 0579.60079

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Inégalités de Sobolev pour un semi-groupe symétrique. (Sobolev inequalities for a symmetric semi-group). (French) Zbl 0579.60079

C. R. Acad. Sci., Paris, Sér. I 301, 411-413 (1985).

Summary: We use the ”iterated gradient” to define the notions of dimension and Ricci curvature associated to a diffusion semi-group. In terms of both these objects, we give a sufficient condition for the generator of a symmetric semi-group to satisfy a Sobolev inequality.

Cited in 4 Reviews

Cited in 16 Documents

MSC:

60J60	Diffusion processes
58J65	Diffusion processes and stochastic analysis on manifolds

Keywords:

Ricci curvature; diffusion semi-group; Sobolev inequality

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