  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.

Functional Analysis