Boundedness of multidimensional Dunkl-Hausdorff operators (Q2179416)

Summary: In the present paper, we introduce the multidimensional Dunkl-Hausdorff operator \(\mathcal{H}_\kappa\) and we give simple sufficient conditions so that these operators be bounded on the weighted Lebesgue spaces \(L_\kappa^p( \mathbb{R}^n)\) and in the Hardy space \(H_\kappa^1( \mathbb{R}^n)\) associated with the Dunkl operators. We also determine the Dunkl-Hausdorff operator \(\mathcal{H}_\kappa^*\) that is adjoint to \(\mathcal{H}_\kappa\).