Scale invariant energy smoothing estimates for the Schrödinger Equation with small Magnetic Potential

Abstract

We consider some scale invariant generalizations of the smoothing estimates for the free Schrödnger equation obtained by Kenig, Ponce and Vega. Applying these estimates and using appropriate commutator estimates, we obtain similar scale invariant smoothing estimates for perturbed Schrödnger equation with small magnetic potential.