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.
Original language | English |
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Pages (from-to) | 3747-3803 |
Number of pages | 57 |
Journal | Journal of the European Mathematical Society |
Volume | 22 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2020 |
Externally published | Yes |
Keywords
- Hölder regularity
- Non-local Dirichlet form
- Parabolic Harnack inequality
- Stability
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Chen, Z. Q., Kumagai, T., & Wang, J. (2020). Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms. Journal of the European Mathematical Society, 22(11), 3747-3803. https://doi.org/10.4171/JEMS/996