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Stability of heat kernel estimates for symmetric non-local Dirichlet forms

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arxiv 1604.04035 v3 pith:E2FXHDXD submitted 2016-04-14 math.PR math.FAmath.MG

classification math.PRmath.FAmath.MG
keywords heatkernelestimatesstabilityalphaestablishinequalitiesprocesses
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Heat kernel estimates for general symmetric pure jump Dirichlet forms

    math.PR 2019-08 conditional novelty 7.0 of 10

    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.

  2. Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms

    math.PR 2019-08 conditional novelty 7.0 of 10

    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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