Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains
Chen, Zhen-Qing ; Song, Renming
Illinois J. Math., Tome 44 (2000) no. 4, p. 138-160 / Harvested from Project Euclid
For a symmetric $\alpha$-stable process $X$ on $\mathbf{R}^{n}$ with $0 \lt \alpha \lt 2$, $n \geq 2$ and a domain $D \subset \mathbf{R}^{n}$, let $L^{D}$ be the infinitesimal generator of the subprocess of $X$ killed upon leaving $D$. For a Kato class function $q$, it is shown that $L^{d}+q$ is intrinsic ultracontractive on a Hölder domain $D$ of order 0. Then this is used to establish the conditional gauge theorem for $X$ on bounded Lipschitz domains in $\mathbf{R}^{n}$. It is also shown that the conditional lifetimes for symmetric stable process in a Hölder domain of order 0 are uniformly bounded.
Publié le : 2000-03-15
Classification:  60J25,  60G51,  60J45
@article{1255984957,
     author = {Chen, Zhen-Qing and Song, Renming},
     title = {Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains},
     journal = {Illinois J. Math.},
     volume = {44},
     number = {4},
     year = {2000},
     pages = { 138-160},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255984957}
}
Chen, Zhen-Qing; Song, Renming. Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains. Illinois J. Math., Tome 44 (2000) no. 4, pp.  138-160. http://gdmltest.u-ga.fr/item/1255984957/