Heat kernel lower Gaussian estimates in the doubling setting without Poincaré inequality. (English) Zbl 1173.58010

Boutayeb, Salahaddine

Publ. Mat., Barc. 53, No. 2, 457-479 (2009).

The author gives a a characterization of the lower Gaussian estimate in terms of certain Hölder inequalities in the settings of a manifold with doubling property satisfying a Gaussian upper estimate of the heat kernel.

Reviewer: Dian K. Palagachev (Bari)

MSC:

58J35	Heat and other parabolic equation methods for PDEs on manifolds
47D07	Markov semigroups and applications to diffusion processes
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

heat kernel; Hölder inequalities; Gaussian estimates

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