On the lacunary spherical maximal function on the Heisenberg group

In this paper we investigate the L p boundedness of lacunary maximal function M H n l a c associated to spherical means A r f taken over Koranyi spheres on Heisenberg group. Closely following an approach used by M. Lacey in Euclidean case, obtain sparse bounds for these functions leading new unweighted and weighted estimates. The key ingredients proof are improving property operator continuity difference − τ y , where ( x ) = 1 is right translation operator.