Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T23:37:45.326Z Has data issue: false hasContentIssue false
  • English
  • Français

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, [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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