Heat Kernel And Riesz Transform Of Schrodinger Operators

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.