{"title":"关于非交换空间上傅里叶乘子的\\(L^p\\) - \\(L^q\\)有界性的注记","authors":"Michael Ruzhansky, Kanat Tulenov","doi":"10.1007/s43036-025-00436-y","DOIUrl":null,"url":null,"abstract":"<div><p>In this work, we study Fourier multipliers on noncommutative spaces. In particular, we show a simple proof of <span>\\(L^p\\)</span>-<span>\\(L^q\\)</span> estimate of Fourier multipliers on general noncommutative spaces associated with semifinite von Neumann algebras. This includes the case of Fourier multipliers on general locally compact unimodular groups.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00436-y.pdf","citationCount":"0","resultStr":"{\"title\":\"A note on \\\\(L^p\\\\)-\\\\(L^q\\\\) boundedness of Fourier multipliers on noncommutative spaces\",\"authors\":\"Michael Ruzhansky, Kanat Tulenov\",\"doi\":\"10.1007/s43036-025-00436-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this work, we study Fourier multipliers on noncommutative spaces. In particular, we show a simple proof of <span>\\\\(L^p\\\\)</span>-<span>\\\\(L^q\\\\)</span> estimate of Fourier multipliers on general noncommutative spaces associated with semifinite von Neumann algebras. This includes the case of Fourier multipliers on general locally compact unimodular groups.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"10 2\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-04-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s43036-025-00436-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-025-00436-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-025-00436-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A note on \(L^p\)-\(L^q\) boundedness of Fourier multipliers on noncommutative spaces
In this work, we study Fourier multipliers on noncommutative spaces. In particular, we show a simple proof of \(L^p\)-\(L^q\) estimate of Fourier multipliers on general noncommutative spaces associated with semifinite von Neumann algebras. This includes the case of Fourier multipliers on general locally compact unimodular groups.
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