Boundedness of the Dunkl–Hausdorff operator in Lebesgue spaces

Jain, Sandhya; Fiorenza, Alberto; Jain, Pankaj

doi:10.1216/rmj.2021.51.2031

Cited by 6 publications

(1 citation statement)

References 17 publications

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“…Next, in [7] authors establish necessary and sufficient conditions on monotone weight functions for the boundedness of special kind Hausdorff operators on weighted Lebesgue spaces. In [23] the boundedness of Dunkl-Hausdorff operator on weighted Lebesgue spaces has been characterized and for a power type weight function the corresponding operator norm has been obtained. Very recently, in [24], the results of [4] were extended for the Dunkl-Hausdorff operator and the boundedness of one-dimensional Hausdorff operator on the cone of non-increasing functions was proved.…”

Section: Introductionmentioning

confidence: 99%

A characterization of two-weight norm inequalities for multidimensional Hausdorff operators on Lebesgue spaces

Bandaliyev,

Aliyeva

2024

Positivity

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In this paper we give necessary conditions and sufficient conditions for the boundedness of multidimensional Hausdorff operator on weighted Lebesgue spaces. In particular, we establish necessary and sufficient conditions for the boundedness of special type multidimensional Hausdorff operator on weighted Lebesgue spaces for monotone radial weight functions. Also, we get similar results for important operators of harmonic analysis which are special cases of the multidimensional Hausdorff operator. The results are illustrated by a number of examples.

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