{"title":"以平滑模量表示的切列尼克-奥普达姆变换的加权可整性","authors":"Salah El Ouadih","doi":"10.1007/s13324-024-00901-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we give sufficient conditions for functions defined on the space <span>\\(L^{p}(\\mathbb {R},d\\mu )\\)</span>, <span>\\(1<p\\le 2\\)</span>, providing the weighted integrability of their Cherednik-Opdam transforms. These results generalize a famous Titchmarsh’s theorem and Younis’ theorem for functions from Lipschitz classes.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 3","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weighted integrability of the Cherednik-Opdam transform in terms of the moduli of smoothness\",\"authors\":\"Salah El Ouadih\",\"doi\":\"10.1007/s13324-024-00901-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we give sufficient conditions for functions defined on the space <span>\\\\(L^{p}(\\\\mathbb {R},d\\\\mu )\\\\)</span>, <span>\\\\(1<p\\\\le 2\\\\)</span>, providing the weighted integrability of their Cherednik-Opdam transforms. These results generalize a famous Titchmarsh’s theorem and Younis’ theorem for functions from Lipschitz classes.</p></div>\",\"PeriodicalId\":48860,\"journal\":{\"name\":\"Analysis and Mathematical Physics\",\"volume\":\"14 3\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Mathematical Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13324-024-00901-6\",\"RegionNum\":3,\"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":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00901-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Weighted integrability of the Cherednik-Opdam transform in terms of the moduli of smoothness
In this paper, we give sufficient conditions for functions defined on the space \(L^{p}(\mathbb {R},d\mu )\), \(1<p\le 2\), providing the weighted integrability of their Cherednik-Opdam transforms. These results generalize a famous Titchmarsh’s theorem and Younis’ theorem for functions from Lipschitz classes.
期刊介绍：
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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