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Riesz transform on manifolds and heat kernel regularity

Pascal Auscher·Thierry Coulhon·Xuan Thinh Duong·Steve Hofmann
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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 $L^p$ 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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Pascal Auscher, Thierry Coulhon, Xuan Thinh Duong, Steve Hofmann. 2004-11-17. Riesz transform on manifolds and heat kernel regularity. https://arxiv.org/abs/math/0411374

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