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

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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 \(\widehat{f}\).

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Acknowledgements

Author thanks the anonymous referee for valuable remarks and references to books connected with quaternion Fourier transform.

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  1. Department of Mechanics and Mathematics, Saratov State University, Saratov, Russian Federation

    Sergey Volosivets

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  1. Sergey Volosivets
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Communicated by Irene Sabadini

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This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Volosivets, S. Boas Type Results for Two-Sided Quaternion Fourier Transform and Uniform Lipschitz Spaces. Complex Anal. Oper. Theory 18, 46 (2024). https://doi.org/10.1007/s11785-024-01491-8

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