Tohoku Mathematical Journal
2020
December
SECOND SERIES VOL. 72, NO. 4

Tohoku Math. J.
72 (2020), 507-526

Title CHARACTERIZATIONS OF HEAT KERNEL ESTIMATES FOR SYMMETRIC NON-LOCAL DIRICHLET FORMS VIA RESISTANCE FORMS

Author Sheng-Hui Chen and Jian Wang

(Received February 4, 2019, revised June 24, 2019)
Abstract. Motivated by [BCK], we obtain new equivalent conditions for two-sided heat kernel estimates of symmetric non-local Dirichlet forms in terms of resistance forms. Characterizations for upper bounds of heat kernel estimates as well as near diagonal lower bounds of Dirichlet heat kernel estimates are also established. These results can be seen as a complement of the recent studies on heat kernel estimates and parabolic Harnack inequalities for symmetric non-local Dirichlet forms in [CKW, CKW2].

Mathematics Subject Classification. Primary 60G52; Secondary 60J25, 60J55, 60J35, 60J75.
Key words and phrases. Symmetric jump process, non-local Dirichlet form, heat kernel, resistance form.

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