On large potential perturbations of the Schrödinger, wave and Klein–Gordon equations

We prove a sharp resolvent estimate in scale invariant norms of Amgon–Hörmander type for a magnetic Schrödinger operator on ℝ^n, n≥3 L=-(∂+iA)^2+V with large potentials A,V of almost critical decay and regularity. The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schrödinger, wave and Klein–Gordon flows associated to L.