Strichartz estimates for the magnetic Schrodinger equation with potentials V of critical decay

We study the Strichartz estimates for the magnetic Schrodinger equation in dimension n3. More specifically, for all Schrodinger admissible pairs (r,q), we establish the estimate when the operator H=-(A)+V satisfies suitable conditions. In the purely electric case A0, we extend the class of potentials V to the Fefferman-Phong class. In doing so, we apply a weighted estimate for the Schrodinger equation developed by Ruiz and Vega. Moreover, for the endpoint estimate of the magnetic case in (3), we investigate an equivalence and find sucient conditions on H and r for which the equivalence holds.