Sharp Lp estimates for Schrodinger groups

Consider a non-negative self-adjoint operator H on L2. We suppose that its heat operator satisfies an off-diagonal algebraic decay estimate, for some exponent p0 between 0 and 2. Then we prove sharp Lp-Lp frequency truncated estimates for the corresponding Schrodinger group, for all p between p0 and p0'. In particular, our results apply to a Laplace operator perturbed by an electromagnetic potential, where the coefficients of the magnetic potential are in L2, while the positive and negative parts of the electric potential are in the local Kato class and in the Kato class, respectively.