Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms

Zhen-Qing Chen; Takashi Kumagai; Jian Wang

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arXiv · 1609.07594

Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms

Zhen-Qing Chen·Takashi Kumagai·Jian Wang

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Abstract

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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BibTeX RIS

Zhen-Qing Chen, Takashi Kumagai, Jian Wang. 2016-09-24. Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms. https://arxiv.org/abs/1609.07594

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