  For 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.
