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Intrinsic ultracontractivity for Lévy processes

Grzywny T.

Probability and Mathematical Statistics

2008

Vol. 28, Fasc. 1

91--106

We prove the intrinsic ultracontractivity for semigroups generated by a large class of symmetric Lévy processes killed on exiting a bounded and connected Lipschitz set under some conditions about the behavior of the Lévy measure in the neighborhood of the origin.

Intrinsic ultracontractivity for symmetric stable processes

Kulczycki T.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 3

325-334

We prove the intrinsic ultracontractivity for the semigroup P[...] generated by the symmetric [alpha]-stable process killed on exiting a bounded open set D. The same property is valid for the alpha-stable Feynman-Kac semigroup T[...] provided D is a gaugeable bounded Lipschitz domain.