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Dunkl–Hausdorff operators on \({BMO}_{\alpha} {(\mathbb{R})}\) and \({W}_{\alpha}^{p,r}{(\mathbb{R})}\)

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Abstract

In the present paper, we have studied the Dunkl–Hausdorff operators \({\mathcal{H}}_{\alpha ,\varphi }\) on the Dunkl-type spaces of functions of bounded mean oscillation \(BMO_{\alpha} ({{\mathbb{R}}})\) and Dunkl-type Sobolev spaces \(W_{\alpha}^{p,r}({{\mathbb{R}}})\). we have determined simple sufficient conditions for these operators to be bounded on these spaces.

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Acknowledgements

The authors would like to thank the anonymous referee, who found misprints as well as suggested valuable improvements to the text.

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  1. Laboratory of Topology, Algebra, Geometry, and Discrete Mathematics, Department of Mathematics, Faculty of Sciences Aïn Chock, University Hassan II, Casablanca, Morocco

    Radouan Daher & Faouaz Saadi

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  1. Radouan Daher
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  2. Faouaz Saadi
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Correspondence to Faouaz Saadi.

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Daher, R., Saadi, F. Dunkl–Hausdorff operators on \({BMO}_{\alpha} {(\mathbb{R})}\) and \({W}_{\alpha}^{p,r}{(\mathbb{R})}\). Rend. Circ. Mat. Palermo, II. Ser 70, 853–860 (2021). https://doi.org/10.1007/s12215-020-00531-4

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  • DOI: https://doi.org/10.1007/s12215-020-00531-4

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