On the equivalence of parabolic Harnack inequalities and heat kernel estimates

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

doi:10.2969/jmsj/06441091

On the equivalence of parabolic Harnack inequalities and heat kernel estimates

Martin T. Barow^*, Alexander Grigor'yan, Takashi Kumagai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

49 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1091-1146
Number of pages	56
Journal	Journal of the Mathematical Society of Japan
Volume	64
Issue number	4
DOIs	https://doi.org/10.2969/jmsj/06441091
Publication status	Published - 2012
Externally published	Yes

Keywords

Caloric function
Dirichlet space
Harnack inequality
Heat kernel estimate
Metric measure space
Volume doubling

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/06441091

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title = "On the equivalence of parabolic Harnack inequalities and heat kernel estimates",

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.",

keywords = "Caloric function, Dirichlet space, Harnack inequality, Heat kernel estimate, Metric measure space, Volume doubling",

author = "Barow, {Martin T.} and Alexander Grigor'yan and Takashi Kumagai",

year = "2012",

doi = "10.2969/jmsj/06441091",

language = "English",

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AU - Barow, Martin T.

AU - Grigor'yan, Alexander

AU - Kumagai, Takashi

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N2 - 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.

AB - 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.

KW - Caloric function

KW - Dirichlet space

KW - Harnack inequality

KW - Heat kernel estimate

KW - Metric measure space

KW - Volume doubling

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JO - Journal of the Mathematical Society of Japan

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ER -

On the equivalence of parabolic Harnack inequalities and heat kernel estimates

Abstract

Keywords

ASJC Scopus subject areas

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