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

Coriasco, Sandro; Ruzhansky, Michael

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

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

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

Résumé
Abstract

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.

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.

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 :

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://www.numdam.org/articles/10.1016/j.crma.2010.07.025/

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