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OFF-DIAGONAL HEAT KERNEL LOWER BOUNDS WITHOUT POINCARÉ

Published online by Cambridge University Press:  17 November 2003

THIERRY COULHON
THIERRY COULHON
Affiliation:
Département de Mathématiques, Université de Cergy-Pontoise, 2 rue Adolphe Chauvin, 95302 Pontoise, Francethierry.coulhon@math.u-cergy.fr
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Abstract

On a manifold with polynomial volume growth satisfying Gaussian upper bounds of the heat kernel, a simple characterization of the matching lower bounds is given in terms of a certain Sobolev inequality. The method also works in the case of so-called sub-Gaussian or sub-diffusive heat kernels estimates, which are typical of fractals. Together with previously known results, this yields a new characterization of the full upper and lower Gaussian or sub-Gaussian heat kernel estimates.

Keywords

58J35 (primary)46E3547D07 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 795 - 816
Copyright
The London Mathematical Society 2003

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Footnotes

Research partially supported by the European Commission (IHP Network ‘Harmonic analysis and related problems’ 2002–2006, contract HPRN-CT-2001-00273-HARP).