A class of generalized integral operators

• Main Authors: Samir Bekkara, Bekkai Messirdi, Abderrahmane Senoussaoui
• Format: Article
• Language: English
• Published: Texas State University 2009-07-01
• Series: Electronic Journal of Differential Equations
• Subjects: Integral operators; L2-boundedness; unbounded Fourier integral operators
• Online Access: http://ejde.math.txstate.edu/Volumes/2009/88/abstr.html

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 $S_{1,1}^{0}(mathbb{R}^{n}imes mathbb{R}^{n})$ and in $igcap_{0< ho <1}S_{ ho ,1}^{0}(mathbb{R}^{n}imes mathbb{R}^{n})$ which cannot be extended to bounded operators in $L^{2}( mathbb{R}^{n})$.