%0 Journal Article
%T Kato smoothing and Strichartz estimates for wave equations with magnetic potentials
%A Piero D'Ancona
%J Mathematics
%D 2014
%I arXiv
%R 10.1007/s00220-014-2169-8
%X Let $H$ be a selfadjoint operator and $A$ a closed operator on a Hilbert space $\mathcal{H}$. If $A$ is $H$-(super)smooth in the sense of Kato-Yajima, we prove that $AH^{-\frac14}$ is $\sqrt{H}$-(super)smooth. This allows to include wave and Klein-Gordon equations in the abstract theory at the same level of generality as Schr\"{o}dinger equations. We give a few applications and in particular, based on the resolvent estimates of Erdogan, Goldberg and Schlag \cite{ErdoganGoldbergSchlag09-a}, we prove Strichartz estimates for wave equations perturbed with large magnetic potentials on $\mathbb{R}^{n}$, $n\ge3$.
%U http://arxiv.org/abs/1403.2537v2