Heat kernel estimates for subordinate Markov processes and their applications

• DOI: 10.1016/j.jde.2022.01.044
• Publication Date: 2022-02-03T00:12:35Z
• Authors: Soobin Cho; Panki Kim; Renming Song; Zoran Vondraček
• Keywords: Heat kernel ; Transition density ; Subordinate Markov process ; Parabolic Harnack inequality ; Green function ; Spectral fractional Laplacian; Mathematics - Analysis of PDEs; Probability (math.PR); FOS: Mathematics; 60J35, 60J50, 60J76; 0101 mathematics; 01 natural sciences; Mathematics - Probability; Analysis of PDEs (math.AP)

43 pages : Some heat kernel estimates are written in different forms<br/>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��lder regularity hold for parabolic functions of such processes, and derive sharp two-sided Green function estimates.<br/>