Geodesic
A class of generalized integral operators
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $L^{2}(\mathbb{R}^{n})$. This permit us in particular to construct a class of Fourier integral operators with bounded symbols in $S_{1,1}^{0}(\mathbb{R}^{n}\times \mathbb{R}^{n})$ and in $\bigcap_{0\rho 1}S_{\rho ,1}^{0} (\mathbb{R}^{n}\times \mathbb{R}^{n})$ which cannot be extended to bounded operators in $L^{2}(\mathbb{R}^{n})$.
Classification : 35S30, 35S05, 47A10, 35P05
Keywords: integral operators, L2-boundedness, unbounded Fourier integral operators 
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     title = {A class of generalized integral operators},
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Bekkara, Samir; Messirdi, Bekkai; Senoussaoui, Abderrahmane. A class of generalized integral operators. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a45/