Scale invariant energy smoothing estimates for the Schr\"odinger   Equation with small Magnetic Potential
  We consider some scale invariant generalizations of the smoothing estimates for the free Schr\"odnger equation obtained by Kenig, Ponce and Vega. Applying these estimates and using appropriate commutator estimates, we obtain similar scale invariant smoothing estimates for perturbed Schr\"odnger equation with small magnetic potential. 
Vladimir Georgiev and Mirko Tarulli