Samir Bekkara, Bekkai Messirdi, Abderrahmane Senoussaoui
Abstract:
In this paper, we introduce a class of generalized integral
operators that includes Fourier integral operators.
We establish some conditions on these operators such that they
do not have bounded extension on
.
This permit us in particular to construct a class of Fourier
integral operators with bounded symbols in
and in
which cannot be extended to bounded operators in
.
Submitted February 12, 2009. Published July 27, 2009.
Math Subject Classifications: 35S30, 35S05, 47A10, 35P05.
Key Words: Integral operators; L2-boundedness;
unbounded Fourier integral operators.
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Samir Bekkara Université des Sciences et de la Technologie d'Oran Faculté des Sciences, Département de Mathématiques, Oran, Algeria email: sbekkara@yahoo.fr |
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Bekkai Messirdi, Abderrahmane Senoussaoui Université d'Oran Es-Sénia, Faculté des Sciences Département de Mathématiques. B.P. 1524 El-Mnaouer, Oran, Algeria email: bmessirdi@univ-oran.dz |
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Abderrahmane Senoussaoui Université d'Oran Es-Sénia, Faculté des Sciences Département de Mathématiques. B.P. 1524 El-Mnaouer, Oran, Algeria email: senoussaoui.abdou@univ-oran.dz |
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