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Contents of PMS, Vol. 28, Fasc. 1,
pages 91 - 106
 

INTRINSIC ULTRACONTRACTIVITY FOR LÉVY PROCESSES

Tomasz Grzywny

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: 60J45.

Key words and phrases: Intrinsic ultracontractivity, Lé vy process, semigroups, strict positivity, transition density, killed process.

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