Journal of the London Mathematical Society



Notes and Papers

OFF-DIAGONAL HEAT KERNEL LOWER BOUNDS WITHOUT POINCARÉ 1


THIERRY COULHON a1
a1 Département de Mathématiques, Université de Cergy-Pontoise, 2 rue Adolphe Chauvin, 95302 Pontoise, France thierry.coulhon@math.u-cergy.fr

Article author query
coulhon t   [Google Scholar] 
 

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.

(Received November 9 2002)
(Revised April 16 2003)

Maths Classification

58J35 (primary); 46E35; 47D07 (secondary).



Footnotes

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