ar X iv : m at h / 06 05 53 3 v 2 [ m at h . PR ] 1 9 Ju n 20 06 Potential Theory of Truncated Stable Processes
نویسنده
چکیده
R d with a Lévy density given by c|x| 1{|x|<1} 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 nonnegative 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.
منابع مشابه
ar X iv : m at h / 06 05 53 3 v 1 [ m at h . PR ] 1 8 M ay 2 00 6 Potential Theory of Truncated Stable Processes
R d with a Lévy density given by c|x| 1{|x|<1} 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 nonnegative functions these processes. We also establish a boundary Harnack principle for nonnegative functions which are harmonic with respect to these processes in bounded conve...
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