In this paper, let \(T_{a,\varphi }\) be a Fourier integral operator with rough amplitude \(a \in {L^\infty }S_\rho ^m\) and rough phase \(\varphi \in {L^\infty }{\Phi ^2}\) which satisfies a new class of rough non-degeneracy condition. When \(0 \leqslant \rho \leqslant 1\), if \(m < \frac{{n(\rho - 1)}}{2} - \frac{{\rho (n - 1)}}{4}\), we obtain that \(T_{a,\varphi }\) is bounded on \({L^2}\). Our main result extends and improves some known results about \({L^2}\) boundedness of Fourier integral operators.

中文翻译：

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关于粗傅立叶积分算子的$$L^2$$有界性

在本文中，令\(T_{a,\varphi }\)为具有粗略幅值\(a\in {L^\infty }S_\rho ^m\)和粗略相位\(\varphi \ {L^\infty }{\Phi ^2}\)满足一类新的粗糙非简并条件。当\(0 \leqslant \rho \leqslant 1\)时，如果\(m < \frac{{n(\rho - 1)}}{2} - \frac{{\rho (n - 1)}}{ 4}\)，我们得到\(T_{a,\varphi }\)以\({L^2}\)为界。我们的主要结果扩展并改进了一些关于傅里叶积分算子\({L^2}\)有界性的已知结果。