@article{23c96a94a3bd42b6b7e2057f6adbb7cb,
title = "Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms",
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 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{\"o}lder regularity of parabolic functions for symmetric non-local Dirichlet forms.",
keywords = "H{\"o}lder regularity, Non-local Dirichlet form, Parabolic Harnack inequality, Stability",
author = "Chen, {Zhen Qing} and Takashi Kumagai and Jian Wang",
note = "Funding Information: The research of Z.-Q. Chen is partially supported by Simons Foundation grant (No. 520542), a Victor Klee Faculty Fellowship at UW, and NNSFC (No. 11731009). The research of T. Ku-magai is partially supported by the Grant-in-Aid for Scientific Research (A) (Nos. 25247007 and 17H01093). The research of J. Wang is partially supported by the National Natural Science Foundation of China (No. 11831014), the Program for Probability and Statistics: Theory and Application (No. IRTL1704), the Program for Innovative Research Teams in Science and Technology in Fujian Province Universities (IRTSTFJ), and the JSPS postdoctoral fellowship (26·04021). Funding Information: We thank Dr. M. Murugan for spotting the inconsistent use of time direction in Definition 1.13(iii) of an earlier version of this paper. We also thank Prof. M. Kassmann and Dr. T. Schulze for pointing out an error in Example 1.3 of an earlier version of this paper. We are grateful to the referees for reading the paper carefully and helpful comments. The research of Z.-Q. Chen is partially supported by Simons Foundation grant (No. 520542), a Victor Klee Faculty Fellowship at UW, and NNSFC (No. 11731009). The research of T. Kumagai is partially supported by the Grant-in-Aid for Scientific Research (A) (Nos. 25247007 and 17H01093). The research of J. Wang is partially supported by the National Natural Science Foundation of China (No. 11831014), the Program for Probability and Statistics: Theory and Application (No. IRTL1704), the Program for Innovative Research Teams in Science and Technology in Fujian Province Universities (IRTSTFJ), and the JSPS postdoctoral fellowship (26?04021). Publisher Copyright: {\textcopyright} 2020 European Mathematical Society Publishing House. All rights reserved.",
year = "2020",
doi = "10.4171/JEMS/996",
language = "English",
volume = "22",
pages = "3747--3803",
journal = "Journal of the European Mathematical Society",
issn = "1435-9855",
publisher = "European Mathematical Society Publishing House",
number = "11",
}