Abstract
For functions \(f\in L^1\left( \mathbb {R}^2,\mathcal {H}\right) \) with the quaternion Fourier transform (QFT) \(\widehat{f}\) we give necessary and sufficient conditions in terms of \(\widehat{f}\) to ensure that f belongs either to one of the generalized Lipschitz classes \(H_{\alpha _1,\alpha _2}^m\) and \(h_{\alpha _1,\alpha _2}^m\) for \(0<\alpha _1,\alpha _2<m\).
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Acknowledgements
The authors thank the referees for the interest they showed to the paper and for their constructive remarks. Thanks also to Professor Rafał Abłamowicz for his number of constructive comments and suggestions which have led to a significant improvement on the presentation and quality of this paper.
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Communicated by Eckhard Hitzer.
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Loualid, E.M., Elgargati, A. & Daher, R. Quaternion Fourier Transform and Generalized Lipschitz Classes. Adv. Appl. Clifford Algebras 31, 14 (2021). https://doi.org/10.1007/s00006-020-01098-0
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DOI: https://doi.org/10.1007/s00006-020-01098-0