, Volume 31, Issue 1, pp 57-77

Intrinsic Ultracontractivity for Stable Semigroups on Unbounded Open Sets

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Abstract

We study the intrinsic ultracontractivity of the semigroup of the isotropic stable process on an unbounded open set. A two-sided estimate of the first eigenfunction of the semigroup is derived. We obtain general geometric conditions for intrinsic ultracontractivity which yield a necessary and sufficient condition for non-degenerate horn-shaped sets.

The research was supported by KBN grant 1 P03A 020 28.