Abstract :
We consider the Schr¨odinger operator Hsy D qq in a bounded domain D 2
in Rd, dG3, with q in the Kato class Kd D. and finite gauge g x.s
Exwexp H0tq Xs.dsx, where Xt.is a Brownian motion and t is the first exit time of
the Brownian motion Xt. from the domain D. Let K and G denote the Green
operators in D for H and D , respectively. We prove that there is a positive 2
constant a such that
