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December 2021 Boundedness of the Dunkl–Hausdorff operator in Lebesgue spaces
Sandhya Jain, Alberto Fiorenza, Pankaj Jain
Rocky Mountain J. Math. 51(6): 2031-2044 (December 2021). DOI: 10.1216/rmj.2021.51.2031

Abstract

In this paper, the Lvp()-boundedness of the Dunkl–Hausdorff operator

Hα,ϕ f(x)=ϕ(t)|t|2α+2fxtdt

has been characterized and for a certain type of weight v, the operator norm Hα,ϕLvp()Lvp() has been obtained. This covers several of the existing results. Analogous results in two dimensions have also been proved.

Citation

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Sandhya Jain. Alberto Fiorenza. Pankaj Jain. "Boundedness of the Dunkl–Hausdorff operator in Lebesgue spaces." Rocky Mountain J. Math. 51 (6) 2031 - 2044, December 2021. https://doi.org/10.1216/rmj.2021.51.2031

Information

Received: 7 January 2021; Revised: 23 April 2021; Accepted: 29 April 2021; Published: December 2021
First available in Project Euclid: 22 March 2022

Digital Object Identifier: 10.1216/rmj.2021.51.2031

Subjects:
Primary: 26D10 , 26D15 , 47B38

Keywords: Dunkl operator , Dunkl–Hausdorff operator , Hausdorff operator , weighted Lebesgue spaces

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 6 • December 2021
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