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arXiv · 2007.11216

Boundedness of Dunkl-Hausdorff operator in Lebesgue spaces

Sandhya Jain·Alberto Fiorenza·Pankaj Jain
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Abstract

In this paper, the $L^p_v(\R)$-boundedness of the Dunkl-Hausdorff operator $\displaystyle H_{\al,ϕ} f(x)=\ent\frac{ |ϕ(t)|}{|t|^{2\al+2}}f\lf(\frac{x}{t}\rh) dt $ has been characterized and for a certain type of weight $v$, the precise value of the norm $\|H_{\al,ϕ}\|_{L^p_v(\R)\to L^p_v(\R)}$ has been obtained. This covers several of the existing results. Analogous results in two dimensions have also been proved.

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Sandhya Jain, Alberto Fiorenza, Pankaj Jain. 2020-07-22. Boundedness of Dunkl-Hausdorff operator in Lebesgue spaces. https://arxiv.org/abs/2007.11216

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