{"title":"\\({L^{p}}\\) 粗糙傅立叶积分算子的估计","authors":"Guoning Wu, Jie Yang","doi":"10.1007/s00013-024-02050-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we obtain the <span>\\({L^p}\\)</span> boundedness of Fourier integral operators with rough amplitude <span>\\(a \\in {L^\\infty }S_\\rho ^m\\)</span> and phase <span>\\(\\varphi \\)</span> that satisfies some generalized derivative estimation and some measure condition. Our main conclusions extend and improve some known results about <span>\\({L^p}\\)</span> boundedness of Fourier integral operators.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"83 - 97"},"PeriodicalIF":0.5000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"\\\\({L^{p}}\\\\) estimates for rough Fourier integral operators\",\"authors\":\"Guoning Wu, Jie Yang\",\"doi\":\"10.1007/s00013-024-02050-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we obtain the <span>\\\\({L^p}\\\\)</span> boundedness of Fourier integral operators with rough amplitude <span>\\\\(a \\\\in {L^\\\\infty }S_\\\\rho ^m\\\\)</span> and phase <span>\\\\(\\\\varphi \\\\)</span> that satisfies some generalized derivative estimation and some measure condition. Our main conclusions extend and improve some known results about <span>\\\\({L^p}\\\\)</span> boundedness of Fourier integral operators.</p></div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":\"124 1\",\"pages\":\"83 - 97\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-024-02050-5\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-02050-5","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
\({L^{p}}\) estimates for rough Fourier integral operators
In this paper, we obtain the \({L^p}\) boundedness of Fourier integral operators with rough amplitude \(a \in {L^\infty }S_\rho ^m\) and phase \(\varphi \) that satisfies some generalized derivative estimation and some measure condition. Our main conclusions extend and improve some known results about \({L^p}\) boundedness of Fourier integral operators.
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Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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