Intrinsic Ultracontractivity , Conditional Lifetimes and Conditional Gauge for Symmetric Stable Processes on Rough Domains

@inproceedings{Chen1998IntrinsicU,
  title={Intrinsic Ultracontractivity , Conditional Lifetimes and Conditional Gauge for Symmetric Stable Processes on Rough Domains},
  author={Zhen-Qing Chen and Renming Song},
  year={1998}
}
For a symmetric c-stable process X on with 0 < o < 2, n > 2 and a domain D C Rn, let LD be the infinitesimal generator of the subprocess of X killed upon leaving D. For a Kato class finction q, it is shown that Lo + q is intrinsic ultracontractive on a Htlder domain D of order 0. Then this is used to establish the conditional gauge theorem for X on bounded Lipschitz domains in Rn. It is also shown that the conditional lifetimes for symmetric stable process in a H/51der domain of order 0 are… CONTINUE READING
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