Boas Type Results for Two-Sided Quaternion Fourier Transform and Uniform Lipschitz Spaces

For the quaternion algebra \({\mathbb {H}}\) $\mathbb{H}$ and \(f:\mathbb R^2\rightarrow {\mathbb {H}}\) $f:{\mathbb{R}}^2\to \mathbb{H}$ , we consider a two-sided quaternion Fourier transform \(\widehat{f}\) $\widehat{f}$ . Necessary and sufficient conditions for f to belong to generalized uniform Lipschitz spaces are given in terms of behavior of \(\widehat{f}\) $\widehat{f}$ .