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

We study the Strichartz estimates for the magnetic Schrödinger equation in dimension n≥3. More specifically, for all Schrödinger admissible pairs (r,q), we establish the estimate (Formula presented.) when the operator H = −Δ_A+V satisfies suitable conditions. In the purely electric case A≡0, we extend the class of potentials V to the Fefferman–Phong class. In doing so, we apply a weighted estimate for the Schrödinger equation developed by Ruiz and Vega. Moreover, for the endpoint estimate of the magnetic case in ℝ³, we investigate an equivalence (Formula presented.) and find sufficient conditions on H and r for which the equivalence holds.