Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains

Zhen Qing Chen, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

For a symmetric α-stable process X on Rn with 0 < α < 2, n ≥ 2 and a domain D ⊂ Rn, let LD be the infinitesimal generator of the subprocess of X killed upon leaving D. For a Kato class function q, it is shown that LD + 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 Rn. It is also shown that the conditional lifetimes for symmetric stable process in a Hölder domain of order 0 are uniformly bounded.

Original languageEnglish (US)
Pages (from-to)138-160
Number of pages23
JournalIllinois Journal of Mathematics
Volume44
Issue number1
DOIs
StatePublished - 2000

ASJC Scopus subject areas

  • Mathematics(all)

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