Riesz transform on manifolds and heat kernel regularity

Details Riesz transform on manifolds and heat kernel regularity Riesz transform on manifolds and heat kernel regularity

2004-11-17

arxiv.org/abs/math/0411374v1

Mathematics

Analysis of PDEs

to appear in Annales de l'Ecole Normale Superieure de Paris

Scientific paper

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.

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