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.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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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.
Stichworte
Heat kernel; non-local Dirichlet form; effective resistance
Erscheinungsjahr
2014
Zeitschriftentitel
Transactions of the American Mathematical Society
Band
366
Ausgabe
12
Seite(n)
6397-6441
ISSN
0002-9947
Page URI
https://pub.uni-bielefeld.de/record/2710500

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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.