On the maximal function associated to the spherical means on the heisenberg group
New York Journal of Mathematics
In this paper we deal with lacunary and full versions of the spherical maximal function on the Heisenberg group Hn, for n ≥ 2. By suitable adaptation of an approach developed by M. Lacey in the Euclidean case, we obtain sparse bounds for these maximal functions, which lead to new unweighted and weighted estimates. In particular, we deduce the Lp boundedness, for 1 < p < ∞, of the lacunary maximal function associated to the spherical means on the Heisenberg group. In order to prove the sparse bounds, we establish Lp − Lq estimates for local (single scale) variants of the spherical means.
Bagchi, Sayan; Hait, Sourav; Roncal, Luz; and Thangavelu, Sundaram, "On the maximal function associated to the spherical means on the heisenberg group" (2021). Journal Articles. 2173.