The Dunkl-Hausdorff operators and the Dunkl continuous wavelets transform

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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Correspondence to Faouaz Saadi.

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Daher, R., Saadi, F. The Dunkl-Hausdorff operators and the Dunkl continuous wavelets transform. J. Pseudo-Differ. Oper. Appl. (2020). https://doi.org/10.1007/s11868-020-00351-1

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Keywords

  • Dunkl transformation
  • Dunkl-Hausdorff operator
  • Riesz transformation
  • Hardy space
  • Dunkl wavelet transformation

Mathematics Subject Classification

  • 47G10
  • 47B38
  • 43A32