Naslov
Two-sided Green function estimates for killed subordinate Brownian motions

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

Izvornik
Proceedings of the london mathematical society (0024-6115) 104 (2012), 5; 927-958

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

Ključne riječi
Green function ; Poisson kernel ; subordinate Brownian motion ; $\kappa$-fat open set ; $C^{; ; ; ; ; ; 1 ; 1}; ; ; ; ; ; $ open set ; symmetric stable process ; relativistic stable process ; harmonic functions ; Harnack inequality ; boundary Harnack principle ; fluctuation theory ; regularly varying function

Sažetak
A subordinate Brownian motion is a L\'evy process which can be obtained by replacing the time of the Brownian motion by an independent subordinator. The infinitesimal generator of a subordinate Brownian motion is $-\phi(-\Delta)$, where $\phi$ is the Laplace exponent of the subordinator. In this paper, we consider a large class of subordinate Brownian motions without diffusion component and with $\phi$ comparable to a regularly varying function at infinity. This class of processes includes symmetric stable processes, relativistic stable processes, sums of independent symmetric stable processes, sums of independent relativistic stable processes, and much more. We give sharp two-sided estimates on the Green functions of these subordinate Brownian motions in any bounded $\kappa$-fat open set $D$. When $D$ is a bounded $C^{; ; ; ; ; ; 1, 1}; ; ; ; ; ; $ open set, we establish an explicit form of the estimates in terms of the distance to the boundary. As a consequence of such sharp Green function estimates, we obtain a boundary Harnack principle in $C^{; ; ; ; ; ; 1, 1}; ; ; ; ; ; $ open sets with explicit rate of decay.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA