Chen, Kumagai, and Wang consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling conditions, and establish the stability of two-sided heat kernel estimates and heat kernel upper bounds. They obtain the stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, they establish the stability of heat kernel estimates for a-stable-like processes even with a equal to or larger than 2 when the underlying spaces have walk dimensions larger than 2, which has been one of the major open problems in this area. Annotation ©2021 Ringgold, Inc., Portland, OR (protoview.com)
