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Kato Smoothing and Strichartz Estimates for Wave Equations with Magnetic Potentials

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Abstract

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 \({AH^{-\frac{1}{4}}}\) is \({\sqrt{H}}\) -(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 \({\mathbb{R}^{n}}\) , n ≥ 3.

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Authors and Affiliations

  1. Dipartimento di Matematica, Unversità di Roma “La Sapienza”, Piazzale A. Moro 2, 00185, Roma, Italy

    Piero D’Ancona

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  1. Piero D’Ancona
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Correspondence to Piero D’Ancona.

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Communicated by W. Schlag

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D’Ancona, P. Kato Smoothing and Strichartz Estimates for Wave Equations with Magnetic Potentials. Commun. Math. Phys. 335, 1–16 (2015). https://doi.org/10.1007/s00220-014-2169-8

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  • DOI: https://doi.org/10.1007/s00220-014-2169-8

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