{"title":"On $$L^2$$ boundedness of rough Fourier integral operators","authors":"Guoning Wu, Jie Yang","doi":"10.1007/s11868-023-00573-z","DOIUrl":null,"url":null,"abstract":"<p>In this paper, let <span>\\(T_{a,\\varphi }\\)</span> be a Fourier integral operator with rough amplitude <span>\\(a \\in {L^\\infty }S_\\rho ^m\\)</span> and rough phase <span>\\(\\varphi \\in {L^\\infty }{\\Phi ^2}\\)</span> which satisfies a new class of rough non-degeneracy condition. When <span>\\(0 \\leqslant \\rho \\leqslant 1\\)</span>, if <span>\\(m < \\frac{{n(\\rho - 1)}}{2} - \\frac{{\\rho (n - 1)}}{4}\\)</span>, we obtain that <span>\\(T_{a,\\varphi }\\)</span> is bounded on <span>\\({L^2}\\)</span>. Our main result extends and improves some known results about <span>\\({L^2}\\)</span> boundedness of Fourier integral operators.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pseudo-Differential Operators and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11868-023-00573-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.