Boundedness of Dunkl-Hausdorff operator in Lebesgue spaces

2020/07/22 by Jain, Sandhya, Alberto Fıorenza, Pankaj Jain +2 · 1 citation
Mathematics · #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2007.11216

Abstract

In this paper, the L^p_v(\R)-boundedness of the Dunkl-Hausdorff operator H_\al,ϕ f(x)=\ent\frac |ϕ(t)||t|^2\al+2f\lf((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^pv(\R)→ L^pv(\R)} has been obtained. This covers several of the existing results. Analogous results in two dimensions have also been proved.

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• Dunkl-Hausdorff operator on weighted Orlicz spaces

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