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We combine Stein's method with a version of Malliavin calculus on the Poissonspace. As a result, we obtain explicit Berry-Ess\'een bounds in Central LimitTheorems (CLTs) involving multiple Wiener-It\^o integrals with respect to ageneral Poisson measure. We provide several applications to CLTs related toOrnstein-Uhlenbeck L\'evy processes.

Stein's method and normal approximation of Poisson functionals