@article{d20e3b8aabfc4db3827da55cd3e7c5c8,
title = "Heat kernel estimates for subordinate Markov processes and their applications",
abstract = "In this paper, we establish sharp two-sided estimates for transition densities of a large class of subordinate Markov processes. As applications, we show that the parabolic Harnack inequality and H{\"o}lder regularity hold for parabolic functions of such processes, and derive sharp two-sided Green function estimates.",
keywords = "Green function, Heat kernel, Parabolic Harnack inequality, Spectral fractional Laplacian, Subordinate Markov process, Transition density",
author = "Soobin Cho and Panki Kim and Renming Song and Zoran Vondra{\v c}ek",
note = "Funding Information: We thank the referee for the comments on the first version of this paper. The third-named author thanks Professor Habib Maagli for pointing a mistake in Theorem 3.10 of [48] , which led to a mistake in Theorem 4.6 there. Part of the research for this paper was done while the third-named author was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China ( 11931004 ) and by the Priority Academic Program Development of Jiangsu Higher Education Institutions . Funding Information: The research of Soobin Cho is supported by the POSCO Science Fellowship of POSCO TJ Park Foundation.This research is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2021R1A4A1027378).Research supported in part by a grant from the Simons Foundation (#429343, Renming Song).Research supported in part by the Croatian Science Foundation under the project 4197 (Zoran Vondra{\v c}ek).We thank the referee for the comments on the first version of this paper. The third-named author thanks Professor Habib Maagli for pointing a mistake in Theorem 3.10 of [48], which led to a mistake in Theorem 4.6 there. Part of the research for this paper was done while the third-named author was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China (11931004) and by the Priority Academic Program Development of Jiangsu Higher Education Institutions. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",
year = "2022",
month = apr,
day = "15",
doi = "10.1016/j.jde.2022.01.044",
language = "English (US)",
volume = "316",
pages = "28--93",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
}