On $$L^2$$ boundedness of rough Fourier integral operators

Pub Date : 2023-12-08 DOI:10.1007/s11868-023-00573-z
Guoning Wu, Jie Yang
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Abstract

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.

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论粗糙傅里叶积分算子的$L^2$$有界性
在本文中,设 \(T_{a,\varphi }\) 是一个傅里叶积分算子,具有粗糙振幅 \(a \in {L^\infty }S_\rho ^m\)和粗糙相位 \(\varphi \in {L^\infty }{Phi ^2}\),它满足一类新的粗糙非退化条件。当 \(0 \leqslant \rho \leqslant 1\) 时,如果 \(m < \frac{n(\rho - 1)}}{2}- 我們可以得到 \(T_{a,\varphi }\) 在 \({L^2}\) 上是有界的。我们的主要结果扩展并改进了关于傅里叶积分算子的 \({L^2}\) 有界性的一些已知结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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