Estimates of heat kernels for non-local regular Dirichlet forms
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AbstractIn this paper we present new heat kernel upper bounds for a certain class of non-local regular Dirichlet forms on metric measure spaces, including fractal spaces. We use a new purely analytic method where one of the main tools is the parabolic maximum principle. We deduce an off-diagonal upper bound of the heat kernel from the on-diagonal one under the volume regularity hypothesis, restriction of the jump kernel and the survival hypothesis. As an application, we obtain two-sided estimates of heat kernels for non-local regular Dirichlet forms with finite effective resistance, including settings with the walk dimension greater than 2.
All Author(s) ListGrigor'yan A., Hu J., Lau K.-S.
Journal nameTransactions of the American Mathematical Society
Year2014
Month1
Day1
Volume Number366
Issue Number12
PublisherAmerican Mathematical Society
Place of PublicationUnited States
Pages6397 - 6441
ISSN0002-9947
eISSN1088-6850
LanguagesEnglish-United Kingdom
KeywordsEffective resistance, Heat kernel, Non-local Dirichlet form

Last updated on 2021-15-01 at 00:57