Hardy space estimates of Hausdorff operators on the Heisenberg group

This is a continuation of a series of works about Hausdorff operator on Hardy spaces in the setting of the Heisenberg group. In this paper, we obtain the boundedness from Lebesgue spaces to Hardy spaces for fractional Hausdorff operators and their compositions with Riesz transforms. We also establish the boundedness for two kinds of special Hausdorff operators, the Hausdorff-Poisson operator and the Hausdorff-Gauss operator, on Hardy spaces.