Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 64, Number 4 (2012), 1091-1146.
On the equivalence of parabolic Harnack inequalities and heat kernel estimates
Martin T. BARLOW, Alexander GRIGOR'YAN, and Takashi KUMAGAI
Full-text: Open access
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.
Article information
Source
J. Math. Soc. Japan, Volume 64, Number 4 (2012), 1091-1146.
Dates
First available in Project Euclid: 29 October 2012
Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1351516770
Digital Object Identifier
doi:10.2969/jmsj/06441091
Mathematical Reviews number (MathSciNet)
MR2998918
Zentralblatt MATH identifier
1281.58016
Subjects
Primary: 58J35: Heat and other parabolic equation methods
Secondary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 31C25: Dirichlet spaces
Keywords
Harnack inequality heat kernel estimate caloric function metric measure space volume doubling Dirichlet space
Citation
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. https://projecteuclid.org/euclid.jmsj/1351516770
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