{"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":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-023-01301-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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:
Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.