A class of generalized integral operators

A class of generalized integral operators

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 integra...

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Veröffentlicht in:Electronic journal of differential equations 2009-07, Vol.2009 (88), p.1-7
Hauptverfasser: Samir Bekkara, Bekkai Messirdi, Abderrahmane Senoussaoui
Format: Artikel
Sprache:eng
Schlagworte:
Integral operators
L2-boundedness
unbounded Fourier integral operators
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Zusammenfassung: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
ISSN:1072-6691