"In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for -stable-like processes even with 2 when the underlying spaces have walk dimensions larger than 2, which has been one of the major open problems in this area"--
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Zhen-Qing Chen, University of Washington, Seattle, WA.
Takashi Kumagai, Kyoto University, Japan.
Jian Wang, Fujian Normal University, Fuzhou, China.
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