Potential theory of truncated stable processes

• Autores: Panki Kim, Renming Song
• Localización: Mathematische zeitschrift, ISSN 0025-5874, Vol. 256, Nº. 1, 2007, págs. 139-173
• Idioma: inglés
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• Resumen

  • For any , a truncated symmetric a-stable process is a symmetric Lévy process in with a Lévy density given by for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality for nonnegative harmonic functions of these processes. We also establish a boundary Harnack principle for nonnegative functions which are harmonic with respect to these processes in bounded convex domains. We give an example of a non-convex domain for which the boundary Harnack principle fails