Spherical maximal operators on Heisenberg groups: Restricted dilation sets
Volume 273 / 2023
Studia Mathematica 273 (2023), 1-28
MSC: Primary 42B25; Secondary 43A80, 42B99, 22E25.
DOI: 10.4064/sm220804-22-6
Published online: 28 September 2023
Abstract
Consider spherical means on the Heisenberg group with a codimension 2 incidence relation, and associated spherical local maximal functions $M_E f$ where the dilations are restricted to a set $E$. We prove $L^p\to L^q$ estimates for these maximal operators; the results depend on various notions of dimension of $E$.
