zbMATH — the first resource for mathematics

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

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
Full Text: Numdam EuDML