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

^*Corresponding author for this work

Research output: Contribution to journal › Review article › peer-review

184 Citations (Scopus)

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 - Nov 2004

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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",

year = "2004",

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T1 - Riesz transform on manifolds and heat kernel regularity

AU - Auscher, Pascal

AU - Coulhon, Thierry

AU - Duong, Xuan Thinh

AU - Hofmann, Steve

PY - 2004/11

Y1 - 2004/11

N2 - 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.

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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U2 - 10.1016/j.ansens.2004.10.003

DO - 10.1016/j.ansens.2004.10.003

M3 - Review article

AN - SCOPUS:14544277476

SN - 0012-9593

VL - 37

SP - 911

EP - 957

JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

IS - 6

ER -

Riesz transform on manifolds and heat kernel regularity

Abstract

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