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arXiv · 2610.18316

Endpoint power weight inequalities for spherical maximal functions

Marco Fraccaroli·Juyoung Lee·Nikou Lei·Joris Roos·Andreas Seeger
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Abstract

We prove sharp $L^p(|x|^α)$ estimate for spherical maximal functions. We resolve the remaining open problem for the full maximal operator for $α=1-d$ and $p<2$ and prove a more general result involving a local version of Assouad dimension of the underlying dilation set. We also make a case study with endpoint bounds for a model case involving convex sequences in $[1,2]$.

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Marco Fraccaroli, Juyoung Lee, Nikou Lei, Joris Roos, Andreas Seeger. 2026-10-13. Endpoint power weight inequalities for spherical maximal functions. https://arxiv.org/abs/2610.18316

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