Kato smoothing and Strichartz estimates for wave equations with magnetic potentials

Let H be a selfadjoint operator and A a closed operator on a Hilbert space H. If A is H-(super)smooth in the sense of Kato-Yajima, we prove that AH^(-1/4) is H^(1/2)-(super)smooth. This allows us to include wave and Klein-Gordon equations in the abstract theory at the same level of generality as Schrödinger equations. We give a few applications and in particular, based on the resolvent estimates of Erdogan, Goldberg and Schlag (Forum Mathematicum 21:687–722, 2009), we prove Strichartz estimates for wave equations perturbed with large magnetic potentials on Rn.