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

IF 0.9 3区 数学 Q2 MATHEMATICS
Guoning Wu, Jie Yang
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引用次数: 0

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.

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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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
59
期刊介绍: The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
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