JournalsjemsVol. 22, No. 11pp. 3747–3803

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

  • Zhen-Qing Chen

    University of Washington, Seattle, USA
  • Takashi Kumagai

    Kyoto University, Japan
  • Jian Wang

    Fujian Normal University, Fuzhou, China
Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms cover
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Abstract

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

Cite this article

Zhen-Qing Chen, Takashi Kumagai, Jian Wang, Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms. J. Eur. Math. Soc. 22 (2020), no. 11, pp. 3747–3803

DOI 10.4171/JEMS/996