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 f to belong to generalized uniform Lipschitz spaces are given in terms of behavior of \(\widehat{f}\) .

中文翻译：

---

两侧四元数傅里叶变换和均匀 Lipschitz 空间的 Boas 类型结果

摘要

对于四元数代数\({\mathbb {H}}\)和\(f:\mathbb R^2\rightarrow {\mathbb {H}}\)，我们考虑双边四元数傅立叶变换\(\widehat {F}\）。f属于广义均匀 Lipschitz 空间的充分必要条件是根据\(\widehat{f}\)的行为给出的。