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arXiv · 2602.17613

Power weight inequalities for spherical maximal functions

Marco Fraccaroli·Joris Roos·Andreas Seeger
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Abstract

This paper is about spherical maximal functions with general dilation sets acting on functions in weighted $L^p(|x|^\alpha)$ spaces. Aside from endpoint cases, a complete description of the allowable ranges of $p$, $\alpha$ is given in terms of the Legendre--Assouad function of the dilation set. This settles, up to endpoints, an open problem of Duoandikoetxea and Seijo.

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Marco Fraccaroli, Joris Roos, Andreas Seeger. 2026-02-19. Power weight inequalities for spherical maximal functions. https://arxiv.org/abs/2602.17613

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