In this paper, we study $n$-dimensional Hardy operator and its dual in mixed radial-angular spaces on Heisenberg group and obtain their sharp bounds by using the rotation method. Furthermore, the sharp bounds of $n$-dimensional weighted Hardy operator and weighted Cesàro operator are also obtained.

In this paper, we first show that the $p$-adic version of maximal function ${\mathcal{M}}_{L\log L}^p$ is equivalent to the maximal function ${\mathcal{M}}^p({\mathcal{M}}^p)$ and that the class of functions for which the maximal commutators and the commutator with the $p$-adic version of maximal function or the maximal sharp function are bounded on the $p$-adic vector spaces are characterized and proved to be the same. Moreover, new pointwise estimates for these operators are proved.