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arXiv · 2610.13326

Sharp power-weight estimates for the fractional spherical maximal operator

Riju Basak·Surjeet Singh Choudhary·Chun-Yen Shen·Daniel Spector
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Abstract

For $0\leqα<n$, let $A_{*}^α$ denote the fractional spherical maximal operator. In this paper we characterise the range of $β$ for which the $L^p-L^q$ power-weight estimate \[\left\|A_{*}^α f\right\|_{L^q(|x|^{qβ})} \leq C \left\|f\right\|_{L^p(|x|^{pβ})}\] holds. In the diagonal case $p=q$, our work gives an affirmative answer to a conjecture of Lee. We prove analogous results for the lacunary fractional spherical maximal operator.

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Riju Basak, Surjeet Singh Choudhary, Chun-Yen Shen, Daniel Spector. 2026-10-09. Sharp power-weight estimates for the fractional spherical maximal operator. https://arxiv.org/abs/2610.13326

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