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Regularity of solutions to the Schrödinger equation. (English) Zbl 0631.42010
Dans cet article, l’A. montre en particulier le résultat suivant sur la régularité des solutions de l’équation de Schrödinger. Avec \(S_ t\) définie sur \({\mathcal S}({\mathbb{R}}^ n)\) par \((S_ tf)(x)=\int_{{\mathbb{R}}^ n}e^{ix\xi}e^{it\xi^ 2}\hat f(\xi)d\xi\) il montre que si \(n\geq 3\) et \(s>\) on a pour toute boule B \((\int_{B}| S^*f(x)|^{1/2}\leq C_ B\| f\|_{H^ s},\forall f\in {\mathcal S}({\mathbb{R}}^ n)\) ou \((S^*f)(x)=\sup_{0<t<1}| S_ tf(x)|.\) Ce résultat améliore des résultats antérieurs de Carleson, Dahlberg, Kenig, Ruiz, Cowling et Stein. Des variantes et des applications sont données.
Reviewer: B.Helffer

MSC:
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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