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Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms
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In this paper, we establish stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms on metric measure spaces under general volume doubling condition. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cutoff Sobolev inequalities, and Poincar\'e inequalities. In particular, we establish the connection between parabolic Harnack inequalities and two-sided heat kernel estimates, as well as with the H\"older regularity of parabolic functions for symmetric non-local Dirichlet forms.
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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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