Hausdorff operators associated with the Opdam--Cherednik transform in Lebesgue spaces

TL;DR

This paper investigates the boundedness of Hausdorff operators linked to the Opdam--Cherednik transform across various Lebesgue spaces, establishing conditions for their boundedness and extending the analysis to grand Lebesgue and quasi-Banach spaces.

Contribution

It introduces the Hausdorff operator associated with the Opdam--Cherednik transform and provides necessary and sufficient conditions for its boundedness in multiple Lebesgue-type spaces.

Findings

Proved boundedness of the Hausdorff operator in Lebesgue spaces

Extended boundedness results to grand Lebesgue and quasi-Banach spaces

Established necessary and sufficient conditions for boundedness

Abstract

In this paper, we introduce the Hausdorff operator associated with the Opdam--Cherednik transform and study the boundedness of this operator in various Lebesgue spaces. In particular, we prove the boundedness of the Hausdorff operator in Lebesgue spaces, in grand Lebesgue spaces, and in quasi-Banach spaces that are associated with the Opdam--Cherednik transform. Also, we give necessary and sufficient conditions for the boundedness of the Hausdorff operator in these spaces.