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Etude des transformations de Riesz dans les variétés riemanniennes à courbure de Ricci minorée. (Study of Riesz transformations in Riemannian manifolds with Ricci curvature bounded from below). (French) Zbl 0629.58018
Sémin. probabilités XXI, Lect. Notes Math. 1247, 137-172 (1987).
[For the entire collection see Zbl 0606.00022.]
Let E be a complete Riemannian manifold and p($$\cdot)$$ a strictly positive weight. Then the operator $$L=\Delta +\nabla (\log p)$$ is selfadjoint on $$L^ 2(p(x)dx)$$. $$L^ p$$-inequalities for this operator are proved under the assumption that the Ricci curvature is bounded from below.
Reviewer: G.Warnecke

##### MSC:
 58J40 Pseudodifferential and Fourier integral operators on manifolds 58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) 58J35 Heat and other parabolic equation methods for PDEs on manifolds
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