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 language | English (US) |
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Pages (from-to) | 138-160 |
Number of pages | 23 |
Journal | Illinois Journal of Mathematics |
Volume | 44 |
Issue number | 1 |
DOIs | |
State | Published - 2000 |
ASJC Scopus subject areas
- General Mathematics