Electron. J. Diff. Eqns., Vol. 2006(2006), No. 26, pp. 1-12.

$L^2$-boundedness and $L^2$-compactness of a class of Fourier integral operators

Bekkai Messirdi, Abderrahmane Senoussaoui

Abstract:
In this paper, we study the $L^2$-boundedness and $L^2$-compactness of a class of Fourier integral operators. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to 0).

Submitted June 10, 2005. Published March 9, 2006.
Math Subject Classifications: 35S30, 35S05, 47A10, 35P05.
Key Words: Fourier integral operators; pseudodifferential operators; symbol and phase; boundedness and compactness.

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Bekkai Messirdi
Université d'Oran Es-Sénia, Faculté des Sciences
Département de Mathématiques
B.P. 1524 El-Mnaouer, Oran, Algeria
email: bmessirdi@univ-oran.dz
Abderrahmane Senoussaoui
Université d'Oran Es-Sénia, Faculté des Sciences
Département de Mathématiques
B.P. 1524 El-Mnaouer, Oran, Algeria
email: asenouss@ulb.ac.be

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