Spherical maximal operators on Heisenberg groups: Restricted dilation sets

Abstract

Consider spherical means on the Heisenberg group with a codimension two 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 $E$.

27 pages, 1 figure; final version to appear in Stud. Math

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