{"title":"四元数变换与广义Lipschitz空间的对偶Boas型结果","authors":"Sergey Volosivets","doi":"10.1007/s00006-023-01301-y","DOIUrl":null,"url":null,"abstract":"<div><p>For the quaternion algebra <span>\\({\\mathbb {H}}\\)</span> and <span>\\(f:\\mathbb R^2\\rightarrow {\\mathbb {H}}\\)</span>, we consider a two-sided quaternion Fourier transform <span>\\({\\widehat{f}}\\)</span>. Necessary and sufficient conditions for <span>\\({\\widehat{f}}\\)</span> to belong to generalized uniform Lipschitz spaces are given in terms of behavior of <i>f</i>.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dual Boas Type Results for the Quaternion Transform and Generalized Lipschitz Spaces\",\"authors\":\"Sergey Volosivets\",\"doi\":\"10.1007/s00006-023-01301-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For the quaternion algebra <span>\\\\({\\\\mathbb {H}}\\\\)</span> and <span>\\\\(f:\\\\mathbb R^2\\\\rightarrow {\\\\mathbb {H}}\\\\)</span>, we consider a two-sided quaternion Fourier transform <span>\\\\({\\\\widehat{f}}\\\\)</span>. Necessary and sufficient conditions for <span>\\\\({\\\\widehat{f}}\\\\)</span> to belong to generalized uniform Lipschitz spaces are given in terms of behavior of <i>f</i>.</p></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00006-023-01301-y\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-023-01301-y","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Dual Boas Type Results for the Quaternion Transform and Generalized Lipschitz Spaces
For the quaternion algebra \({\mathbb {H}}\) and \(f:\mathbb R^2\rightarrow {\mathbb {H}}\), we consider a two-sided quaternion Fourier transform \({\widehat{f}}\). Necessary and sufficient conditions for \({\widehat{f}}\) to belong to generalized uniform Lipschitz spaces are given in terms of behavior of f.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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