On the boundedness of Fourier integral operators on $ {L}^{p}({\mathbb{R}}^{n})$

Sandro Coriasco; Michael Ruzhansky

doi:10.1016/j.crma.2010.07.025

Mathematical Analysis/Harmonic Analysis

On the boundedness of Fourier integral operators on

L^{p} (R^{n})

[Sur la continuité des opérateurs intégraux de Fourier sur

L^{p} (R^{n})

]

Présenté par : Jean-Michel Bony

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

Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 847-851.

Abstract (VO)
Résumé

The aim of this Note is to present global $L^{p}$ boundedness results for Fourier integral operators in $R^{n}$ . The main question is what are the decay conditions on the amplitudes for the operators to be bounded on $L^{p} (R^{n})$ . 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 $L^{p} (R^{n})$ . 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 : 2010-03-29
Accepté le : 2010-07-26
Publié le : 2010-08-01

DOI : 10.1016/j.crma.2010.07.025

Affiliations des auteurs :

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

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     journal = {Comptes Rendus. Math\'ematique},
     pages = {847--851},
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     year = {2010},
     doi = {10.1016/j.crma.2010.07.025},
     language = {en},
}

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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.025/

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