Ricerc@Sapienza

We prove a sharp resolvent estimate in scale invariant norms of Amgon–Hörmander type for a magnetic Schrödinger operator on Rn, 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.