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arXiv · 2412.09390

Spherical maximal operators with fractal sets of dilations on radial functions

David Beltran·Joris Roos·Andreas Seeger
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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 $E$.

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David Beltran, Joris Roos, Andreas Seeger. 2024-12-12. Spherical maximal operators with fractal sets of dilations on radial functions. https://arxiv.org/abs/2412.09390

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