On the equivalence of parabolic Harnack inequalities and heat kernel estimates

Martin T. Barlow; Alexander Grigor'yan; Takashi Kumagai

doi:10.2969/jmsj/06441091

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

On the equivalence of parabolic Harnack inequalities and heat kernel estimates

Martin T. Barlow, Alexander Grigor'yan, Takashi Kumagai

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

JOURNAL FREE ACCESS

2012 Volume 64 Issue 4 Pages 1091-1146

DOI https://doi.org/10.2969/jmsj/06441091

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Abstract

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.

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