Comptes Rendus
Mathematical Analysis/Harmonic Analysis
On the boundedness of Fourier integral operators on Lp(Rn)
Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 847-851.

The aim of this Note is to present global Lp boundedness results for Fourier integral operators in Rn. The main question is what are the decay conditions on the amplitudes for the operators to be bounded on Lp(Rn). Results under different sets of assumptions on phase functions and amplitudes are presented.

Dans cette Note nous présentons des estimations globales pour les opérateurs intégraux de Fourier dans les espaces Lp(Rn). Les questions d'intérêt sont les conditions des décroissance pour les amplitudes. Les résultats sont présentés sous des conditions différentes sur la fonction de phase et l'amplitude.

Published online:
DOI: 10.1016/j.crma.2010.07.025

Sandro Coriasco 1; Michael Ruzhansky 2

1 Dipartimento di Matematica, Università di Torino, V. C. Alberto, n. 10, Torino, Italy
2 Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom
     author = {Sandro Coriasco and Michael Ruzhansky},
     title = {On the boundedness of {Fourier} integral operators on $ {L}^{p}({\mathbb{R}}^{n})$},
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Sandro Coriasco; Michael Ruzhansky. On the boundedness of Fourier integral operators on $ {L}^{p}({\mathbb{R}}^{n})$. Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 847-851. doi : 10.1016/j.crma.2010.07.025.

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