Riesz transform on manifolds and heat kernel regularity
Analysis of PDEs
2007-05-23 v1 Classical Analysis and ODEs
Differential Geometry
Abstract
One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is bounded on such a manifold, for ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certain estimate in the same interval of 's.
Cite
@article{arxiv.math/0411374,
title = {Riesz transform on manifolds and heat kernel regularity},
author = {Pascal Auscher and Thierry Coulhon and Xuan Thinh Duong and Steve Hofmann},
journal= {arXiv preprint arXiv:math/0411374},
year = {2007}
}
Comments
to appear in Annales de l'Ecole Normale Superieure de Paris