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Boas-type theorems for the free metaplectic transform

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Abstract

In this study, we focus on the free metaplectic transform and its implications on the properties of functions. The free metaplectic transform is a generalization of the Fourier transform that allows us to analyze the behavior of functions in the metaplectic domain. F. Moricz previously investigated the properties of functions \(f\in L^1({\mathbb {R}})\) whose Fourier transforms \(\widehat{f}\) belong to \(L^1({\mathbb {R}})\). He established certain sufficient conditions based on \(\widehat{f}\) to determine whether f belongs to the Lipschitz classes \({\text {Lip}}(\gamma )\) and \({\text {lip}}(\gamma )\), where \(0 < \gamma \le 1\), or the Zygmund classes \({\text {Zyg}}(\gamma )\) and \({\text {zyg}}(\gamma )\), where \(0 < \gamma \le 2\). In this study, our aim is to extend these findings and explore the properties of functions in relation to the free metaplectic transform.

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Acknowledgements

The authors express their gratitude to the referee for their engagement and valuable constructive feedback.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences Ain Chock, University of Hassan II, Casablanca, Morocco

    Abdelghani El Gargati & Imane Berkak

  2. Chouaib Doukkali University of El Jadida, Natl Sch Appl Sci, Sci Engineer Lab Energy, El Jadida, Morocco

    El Mehdi Loualid

Authors
  1. Abdelghani El Gargati
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  2. Imane Berkak
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  3. El Mehdi Loualid
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Correspondence to El Mehdi Loualid.

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Gargati, A.E., Berkak, I. & Loualid, E.M. Boas-type theorems for the free metaplectic transform. Ann Univ Ferrara (2024). https://doi.org/10.1007/s11565-024-00522-8

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