2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112857For any 0 < alpha <2, a truncated symmetric alpha-stable process is a symmetric Levy process in R^d with a Levy density given by c|x|^{-d-alpha} 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 convex domains. We give an example of a non-convex domain for which the boundary Harnack principle fails.35 page, to appear in Mathematische ZeitschriftProbability60J45text