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Stability of heat kernel estimates for symmetric non-local Dirichlet forms
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abstract
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 $\alpha$-stable-like processes even with $\alpha\ge 2$ when the underlying spaces have walk dimensions larger than $2$, which has been one of the major open problems in this area.
Forward citations
Cited by 2 Pith papers
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Heat kernel estimates for general symmetric pure jump Dirichlet forms
For symmetric pure jump Dirichlet forms, two-sided heat kernel estimates, jumping kernel bounds, and Sobolev/Faber-Krahn/Poincaré inequalities are mutually stable under the two-scale assumptions.
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Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms
The authors characterize two-sided heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms with both local and non-local parts under volume doubling and mild scale-function assumptions.
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