INTRINSIC ULTRACONTRACTIVITY FOR LÉVY PROCESSES
Abstract: 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.
2000 AMS Mathematics Subject Classification: Primary: 60J25, 47D07; Secondary:
Key words and phrases: Intrinsic ultracontractivity, Lé vy process, semigroups, strict
positivity, transition density, killed process.