  The goal of this article is twofold: in a first part, we prove Gaussian
estimates for the heat kernel of Schr{\"o}dinger operators delta + V whose
potential V is "small at infinity" in an integral sense. In a second part, we
prove sharp boundedness result for the associated Riesz transform with
potential d(delta+V) --1/2. A characterization of p-hyperbolicity, which is of
independent interest, is also proved.
