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arXiv · 2609.17246

Improved weighted bounds for the strong maximal function

Sheldy Ombrosi·Guillermo Rey
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Abstract

We improve the exponents of the $A_p$ constant in the strong and weak-type weighted bounds for the strong maximal function, for every $1 < p <\infty$ and every dimension $d \geq 2$. In dimension two, the strong and weak $L^2(w)$ exponents improve from $2$ to $7/4$ and from $3/2$ to $5/4$, respectively. The proof exploits the geometry of pairwise intersections of antichains of dyadic rectangles.

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Sheldy Ombrosi, Guillermo Rey. 2026-09-15. Improved weighted bounds for the strong maximal function. https://arxiv.org/abs/2609.17246

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