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 $L^p$ bounded on such a manifold, for $p$ ranging in an open interval above $2$, if and only if the gradient of the heat kernel satisfies a certain $L^p$ estimate in the same interval of $p$'s.
Publié le : 2004-11-16
Classification:
58J35, 42B20,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA],
[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]
@article{hal-00003304,
author = {Auscher, Pascal and Coulhon, Thierry and Thinh Duong, Xuan and Hofmann, Steve},
title = {Riesz transform on manifolds and heat kernel regularity},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00003304}
}
Auscher, Pascal; Coulhon, Thierry; Thinh Duong, Xuan; Hofmann, Steve. Riesz transform on manifolds and heat kernel regularity. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003304/