Spherical maximal operators on Heisenberg groups: Restricted dilation sets

Published 4 Aug 2022 in math.CA | (2208.02774v2)

Abstract: Consider spherical means on the Heisenberg group with a codimension two incidence relation, and associated spherical local maximal functions $M_Ef$ 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 $E$.

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