{"title":"基于多项式分划的振荡积分算子的尖锐估计","authors":"L. Guth, J. Hickman, Marina Iliopoulou","doi":"10.4310/acta.2019.v223.n2.a2","DOIUrl":null,"url":null,"abstract":"The sharp range of $L^p$-estimates for the class of H\\\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":" ","pages":""},"PeriodicalIF":4.9000,"publicationDate":"2017-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"55","resultStr":"{\"title\":\"Sharp estimates for oscillatory integral operators via polynomial partitioning\",\"authors\":\"L. Guth, J. Hickman, Marina Iliopoulou\",\"doi\":\"10.4310/acta.2019.v223.n2.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The sharp range of $L^p$-estimates for the class of H\\\\\\\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments.\",\"PeriodicalId\":50895,\"journal\":{\"name\":\"Acta Mathematica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":4.9000,\"publicationDate\":\"2017-10-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"55\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/acta.2019.v223.n2.a2\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/acta.2019.v223.n2.a2","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Sharp estimates for oscillatory integral operators via polynomial partitioning
The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments.
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