실적년도 | 2014년 |
---|---|
논문구분 | 국외 |
총저자 | Zhen-Qing Chen, Panki Kim, Renming Song |
학술지명 | Proceedings of the London Mathematical Society |
권(Vol.) | 109 |
호(No.) | 1 |
게재년월 | 2014년 7월 |
Impact Factor | |
SCI 등재 | SCI |
비고 |
In this paper, we consider a large class of purely discontinuous rotationally symmetric Lévy processes. We establish sharp two-sided estimates for the transition densities of such processes killed upon leaving an open set $D$. When $D$ is a κ-fat open set, the sharp two-sided estimates are given in terms of surviving probabilities and the global transition density of the Lévy process. When $D$ is a $C^{1,1}$ open set and the Lévy exponent of the process is given by Ψ(ξ) = φ(|ξ|2) with φ being a complete Bernstein function satisfying a mild growth condition at infinity, our two-sided estimates are explicit in terms of Ψ, the distance function to the boundary of $D$ and the Lévy density of $X$. This gives an affirmative answer to the conjecture posted in Chen, Kim and Song (Global heat kernel estimates for relativistic stable processes in half-space-like open sets. Potential Anal. 36 (2012) 235–261). Our results are the first sharp two-sided Dirichlet heat kernel estimates for a large class of symmetric Lévy processes with general Lévy exponents. We also derive an explicit lower bound estimate for symmetric Lévy processes on ${\Bbb R}^d$ in terms of their Lévy exponents.