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Growth properties of the q-Dunkl transform in the space \(L^{p}_{q,\alpha }({\mathbb {R}}_{q},|x|^{2\alpha +1}d_{q}x)\)

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Abstract

Our aim in this work is to prove an analogue of Titchmarsh’s theorem [19, Theorem 84] and Younis’s theorem [20, Theorem 3.3] on the image under the q-Dunkl transform of a class functions satisfying the q-Dunkl–Lipschitz condition in the space \(L^{p}_{q,\alpha }({\mathbb {R}}_{q},|x|^{2\alpha +1}d_{q}x)\), where \(1<p\le 2\). For this purpose, we use the generalized q-Dunkl translation.

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Acknowledgements

The authors are grateful to the referees for the useful comments and suggestions in improving the presentation of the paper.

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

    Radouan Daher & Othman Tyr

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  1. Radouan Daher
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  2. Othman Tyr
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Correspondence to Othman Tyr.

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Daher, R., Tyr, O. Growth properties of the q-Dunkl transform in the space \(L^{p}_{q,\alpha }({\mathbb {R}}_{q},|x|^{2\alpha +1}d_{q}x)\). Ramanujan J 57, 119–134 (2022). https://doi.org/10.1007/s11139-021-00387-x

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  • DOI: https://doi.org/10.1007/s11139-021-00387-x

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