The second-order gradient estimates for the \(V\)-heat kernel and its applications. (English) Zbl 1527.35102
Summary: In this paper, we derive the second-order gradient estimates for the \(V\)-heat kernel on complete Riemannian manifolds with Bakry-Emery Ricci curvature bounded from below. Applying these estimates, we proved that the \(f\)-Riesz transform on a complete manifold with nonnegative \(N\)-Bakry-Emery Ricci curvature is of weak type (1,1).
MSC:
| 35B45 | A priori estimates in context of PDEs |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35K08 | Heat kernel |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
Keywords:
gradient estimate; \(V\)-Laplace operator; \(V\)-heat kernel; Bakry-Emery curvature; \(f\)-Riesz transformReferences:
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