{"title":"螺旋最大函数的非对角估计值","authors":"David Beltran, Jennifer Duncan, Jonathan Hickman","doi":"10.1112/plms.12594","DOIUrl":null,"url":null,"abstract":"The optimal <span data-altimg=\"/cms/asset/360821de-57a8-46af-8e3f-181682369c83/plms12594-math-0001.png\"></span><math altimg=\"urn:x-wiley:00246115:media:plms12594:plms12594-math-0001\" display=\"inline\" location=\"graphic/plms12594-math-0001.png\">\n<semantics>\n<mrow>\n<msup>\n<mi>L</mi>\n<mi>p</mi>\n</msup>\n<mo>→</mo>\n<msup>\n<mi>L</mi>\n<mi>q</mi>\n</msup>\n</mrow>\n$L^p \\rightarrow L^q$</annotation>\n</semantics></math> mapping properties for the (local) helical maximal function are obtained, except for endpoints. The proof relies on tools from multilinear harmonic analysis and, in particular, a localised version of the Bennett–Carbery–Tao restriction theorem.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Off-diagonal estimates for the helical maximal function\",\"authors\":\"David Beltran, Jennifer Duncan, Jonathan Hickman\",\"doi\":\"10.1112/plms.12594\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The optimal <span data-altimg=\\\"/cms/asset/360821de-57a8-46af-8e3f-181682369c83/plms12594-math-0001.png\\\"></span><math altimg=\\\"urn:x-wiley:00246115:media:plms12594:plms12594-math-0001\\\" display=\\\"inline\\\" location=\\\"graphic/plms12594-math-0001.png\\\">\\n<semantics>\\n<mrow>\\n<msup>\\n<mi>L</mi>\\n<mi>p</mi>\\n</msup>\\n<mo>→</mo>\\n<msup>\\n<mi>L</mi>\\n<mi>q</mi>\\n</msup>\\n</mrow>\\n$L^p \\\\rightarrow L^q$</annotation>\\n</semantics></math> mapping properties for the (local) helical maximal function are obtained, except for endpoints. The proof relies on tools from multilinear harmonic analysis and, in particular, a localised version of the Bennett–Carbery–Tao restriction theorem.\",\"PeriodicalId\":49667,\"journal\":{\"name\":\"Proceedings of the London Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-04-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1112/plms.12594\",\"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":"Proceedings of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1112/plms.12594","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Off-diagonal estimates for the helical maximal function
The optimal mapping properties for the (local) helical maximal function are obtained, except for endpoints. The proof relies on tools from multilinear harmonic analysis and, in particular, a localised version of the Bennett–Carbery–Tao restriction theorem.
期刊介绍：
The Proceedings of the London Mathematical Society is the flagship journal of the LMS. It publishes articles of the highest quality and significance across a broad range of mathematics. There are no page length restrictions for submitted papers.
The Proceedings has its own Editorial Board separate from that of the Journal, Bulletin and Transactions of the LMS.
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