ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS

Grigoryan A, Hu J, Lau K-S (2014)
Transactions of the American Mathematical Society 366(12): 6397-6441.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
In 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.
Erscheinungsjahr
Zeitschriftentitel
Transactions of the American Mathematical Society
Band
366
Ausgabe
12
Seite(n)
6397-6441
ISSN
PUB-ID

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Grigoryan A, Hu J, Lau K-S. ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS. Transactions of the American Mathematical Society. 2014;366(12):6397-6441.
Grigoryan, A., Hu, J., & Lau, K. - S. (2014). ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS. Transactions of the American Mathematical Society, 366(12), 6397-6441.
Grigoryan, A., Hu, J., and Lau, K. - S. (2014). ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS. Transactions of the American Mathematical Society 366, 6397-6441.
Grigoryan, A., Hu, J., & Lau, K.-S., 2014. ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS. Transactions of the American Mathematical Society, 366(12), p 6397-6441.
A. Grigoryan, J. Hu, and K.-S. Lau, “ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS”, Transactions of the American Mathematical Society, vol. 366, 2014, pp. 6397-6441.
Grigoryan, A., Hu, J., Lau, K.-S.: ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS. Transactions of the American Mathematical Society. 366, 6397-6441 (2014).
Grigoryan, Alexander, Hu, Jiaxin, and Lau, Ka-Sing. “ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS”. Transactions of the American Mathematical Society 366.12 (2014): 6397-6441.