Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 88, pp. 1-7.

Title: A class of generalized integral operators

Authors: Samir Bekkara   (Univ. d'Oran, Oran, Algeria)
         Bekkai Messirdi (Univ. d'Oran, Es-Senia, Algeria)
	 Abderrahmane Senoussaoui (Univ. d'Oran, Es-Senia, Algeria)

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 $L^{2}(\mathbb{R}^{n})$.
 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
 $L^{2}( \mathbb{R}^{n})$.
  
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.