{"title":"关于一般测度的高维Kakeya极大函数的范数估计","authors":"Anthony Gauvan","doi":"10.14321/realanalexch.48.2.1671696175","DOIUrl":null,"url":null,"abstract":"We generalize Mitsis’s work to higher dimensions and give application to a conditional estimate concerning Omega-Kakeya sets. Also, following Bourgain's arithmetic argument, we improve concrete bound on the Hausdorff dimension of an Omega-Kakeya set.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"22 1","pages":"0"},"PeriodicalIF":0.1000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Norm Estimates for the Kakeya Maximal Function in High Dimensions with Respect to General Measures\",\"authors\":\"Anthony Gauvan\",\"doi\":\"10.14321/realanalexch.48.2.1671696175\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We generalize Mitsis’s work to higher dimensions and give application to a conditional estimate concerning Omega-Kakeya sets. Also, following Bourgain's arithmetic argument, we improve concrete bound on the Hausdorff dimension of an Omega-Kakeya set.\",\"PeriodicalId\":44674,\"journal\":{\"name\":\"Real Analysis Exchange\",\"volume\":\"22 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Real Analysis Exchange\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14321/realanalexch.48.2.1671696175\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Real Analysis Exchange","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14321/realanalexch.48.2.1671696175","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Norm Estimates for the Kakeya Maximal Function in High Dimensions with Respect to General Measures
We generalize Mitsis’s work to higher dimensions and give application to a conditional estimate concerning Omega-Kakeya sets. Also, following Bourgain's arithmetic argument, we improve concrete bound on the Hausdorff dimension of an Omega-Kakeya set.