BOUNDEDNESS OF DUNKL-HAUSDORFF OPERATOR FOR RADIALLY DECREASING FUNCTIONS AND MONOTONE WEIGHTS ON \(\mathbb {R}^{n}\)

We characterize the \({L^{p}_{v}}(\mathbb {R}^{n})\) $L_v^p({\mathbb{R}}^n)$ - \({L^{q}_{u}}(\mathbb {R}^{n})\) $L_u^q({\mathbb{R}}^n)$ boundedness of the Dunkl-Hausdorff operator for radially decreasing functions. Both the cases \(1< p \le q < \infty\) $1<p\le q<\infty$ as well as \(1< q< p < \infty\) $1<q<p<\infty$ have been discussed. For \(p=q\) $p=q$ , the boundedness has also been characterized in case the weights are radially monotone.