Geodesic
Mathematical Analysis/Harmonic Analysis
On the boundedness of Fourier integral operators on Lp(Rn)
[Sur la continuité des opérateurs intégraux de Fourier sur Lp(Rn)]

Présenté par : Jean-Michel Bony

Coriasco, Sandro1 ; Ruzhansky, Michael2
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
Comptes Rendus. Mathématique, Tome 348 (2010) no. 15-16, pp. 847-851.

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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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.07.025

Coriasco, Sandro 1 ; Ruzhansky, Michael 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 
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Coriasco, Sandro; Ruzhansky, Michael. On the boundedness of Fourier integral operators on $ {L}^{p}({\mathbb{R}}^{n})$. Comptes Rendus. Mathématique, Tome 348 (2010) no. 15-16, pp. 847-851. doi : 10.1016/j.crma.2010.07.025. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2010.07.025/

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