{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11868-023-00573-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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.