Abstract
In the present paper, we prove the boundedness of Dunkl-Hausdorff operators in space \(L^p_{\alpha }({\mathbb {R}})\) and in the Hardy space \(H^{1}_{\alpha }({\mathbb {R}})\) associated with the Dunkl operators, investigate continuous Dunkl wavelet transformation, and obtain some useful results. The relation between Dunkl wavelet transformation and Dunkl-Hausdorff operator is also established.
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Acknowledgements
The authors would like to thank the anonymous referee and F. Rouviére, who both found misprints as well as suggested valuable improvements to the text.
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Daher, R., Saadi, F. The Dunkl-Hausdorff operators and the Dunkl continuous wavelets transform. J. Pseudo-Differ. Oper. Appl. 11, 1821–1831 (2020). https://doi.org/10.1007/s11868-020-00351-1
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DOI: https://doi.org/10.1007/s11868-020-00351-1
Keywords
- Dunkl transformation
- Dunkl-Hausdorff operator
- Riesz transformation
- Hardy space
- Dunkl wavelet transformation