Riesz transform on manifolds and heat kernel regularity

Pascal Auscher; Thierry Coulhon; Xuan Thinh Duong; Steve Hofmann

doi:10.1016/j.ansens.2004.10.003

Riesz transform on manifolds and heat kernel regularity

Pascal Auscher
, Thierry Coulhon
, Xuan Thinh Duong
, Steve Hofmann

Université Paris-Saclay
CY Cergy Paris Université
Macquarie University
University of Missouri

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	911-957
Number of pages	47
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	37
Issue number	6
DOIs	https://doi.org/10.1016/j.ansens.2004.10.003
Publication status	Published - 1 Jan 2004
Externally published	Yes

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10.1016/j.ansens.2004.10.003

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title = "Riesz transform on manifolds and heat kernel regularity",

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 Lp 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 Lp estimate in the same interval of p's.",

author = "Pascal Auscher and Thierry Coulhon and Duong, \{Xuan Thinh\} and Steve Hofmann",

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AU - Duong, Xuan Thinh

AU - Hofmann, Steve

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AB - 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 Lp 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 Lp estimate in the same interval of p's.

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DO - 10.1016/j.ansens.2004.10.003

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SN - 0012-9593

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JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

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ER -

Riesz transform on manifolds and heat kernel regularity

Abstract

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