Spherical maximal operators with fractal sets of dilations on radial functions
Volume 289 / 2026
Studia Mathematica 289 (2026), 1-32
MSC: Primary 42B25; Secondary 28A80
DOI: 10.4064/sm241213-27-2
Published online: 18 June 2026
Abstract
For a given set of dilations $E\subset [1,2]$, Lebesgue space mapping properties of the spherical maximal operator with dilations restricted to $E$ are studied when acting on radial functions. In higher dimensions, the type set only depends on the upper Minkowski dimension of $E$, and in this case complete endpoint results are obtained. In two dimensions we determine the closure of the $L^p\to L^q$ type set for every given set $E$ in terms of a dimensional spectrum closely related to the upper Assouad spectrum of $E$.
