Journal of the Mathematical Society of Japan

On the equivalence of parabolic Harnack inequalities and heat kernel estimates

Martin T. BARLOW, Alexander GRIGOR'YAN, and Takashi KUMAGAI

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We prove the equivalence of parabolic Harnack inequalities and sub-Gaussian heat kernel estimates in a general metric measure space with a local regular Dirichlet form.

Article information

J. Math. Soc. Japan, Volume 64, Number 4 (2012), 1091-1146.

First available in Project Euclid: 29 October 2012

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Zentralblatt MATH identifier

Primary: 58J35: Heat and other parabolic equation methods
Secondary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 31C25: Dirichlet spaces

Harnack inequality heat kernel estimate caloric function metric measure space volume doubling Dirichlet space


BARLOW, Martin T.; GRIGOR'YAN, Alexander; KUMAGAI, Takashi. On the equivalence of parabolic Harnack inequalities and heat kernel estimates. J. Math. Soc. Japan 64 (2012), no. 4, 1091--1146. doi:10.2969/jmsj/06441091.

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