Potential Analysis

, Volume 31, Issue 1, pp 57–77

Intrinsic Ultracontractivity for Stable Semigroups on Unbounded Open Sets


DOI: 10.1007/s11118-009-9125-9

Cite this article as:
Kwaśnicki, M. Potential Anal (2009) 31: 57. doi:10.1007/s11118-009-9125-9


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.


Intrinsic ultracontractivityIsotropic stable processFirst eigenfunction

Mathematics Subject Classifications (2000)

Primary 47D0760G52Secondary 60J45

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceWrocław University of TechnologyWrocławPoland