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

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 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.

61 pages, 1 figure; arXiv version

Cited by in corpus (4)

• Elliptic Harnack inequalities for symmetric non-local Dirichlet forms
• Heat kernel estimates for symmetric jump processes with mixed polynomial growths
• Estimates of Dirichlet heat kernels for subordinate Brownian motions
• Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions