Geodesic
A class of generalized integral operators
Electronic journal of differential equations, Tome 2009 (2009)
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 
@article{EJDE_2009__2009__a45,
     author = {Bekkara,  Samir and Messirdi,  Bekkai and Senoussaoui,  Abderrahmane},
     title = {A class of generalized integral operators},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1177.35267},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a45/}
}
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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/