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.

中文翻译：

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四元数变换和广义 Lipschitz 空间的双 Boas 类型结果

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\({\宽帽{f}}\)。根据f的行为给出了\({\widehat{f}}\)属于广义均匀 Lipschitz 空间的充分必要条件。