Hausdorff operators on the Heisenberg group

This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group Hn. The sharp bounds for the strong type (p, p) (1 . p . .) estimates of n-dimensional Hausdorff operators on Hn are obtained. The sharp bounds for strong (p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on Hn. The weak type (p, p) (1 . p..) estimates are also obtained. Keywords Hausdorff operator, Heisenberg group, multilinear, sharp estimate