Naslov
Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings

Autori
Cho, Soobin ; Kim, Panki ; Song, Renming ; Vondraček, Zoran

Izvornik
Journal de mathématiques pures et appliquées (0021-7824) 143 (2020); 208-256

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Dirichlet heat kernel, transition density, critical killings, potential, additive functional, Kato class

Sažetak
In this paper we discuss non-local operators with killing potentials, which may not be in the standard Kato class. We first discuss factorization of their Dirichlet heat kernels in metric measure spaces. Then we establish explicit estimates of the Dirichlet heat kernels under critical killings in $C^{; ; 1, 1}; ; $ open subsets of $\R^d$ or in $\R^d\setminus\{; ; 0\}; ; $. The decay rates of our explicit estimates come from the values of the multiplicative constants in the killing potentials. Our method also provides an alternative and unified proof of the main results of \cite{; ; CKS10a, CKS10b, CKS-AOP}; ; .

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA