PreprintCC BY 4.0arXiv
Improved weighted bounds for the strong maximal function
Abstract
We improve the exponents of the Ap constant in the strong and weak-type weighted bounds for the strong maximal function, for every 1 < p <∞ and every dimension d ≥ 2. In dimension two, the strong and weak L2(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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BibTeX
@misc{ombrosi2026improved,
title = {{Improved weighted bounds for the strong maximal function}},
author = {Sheldy Ombrosi and Guillermo Rey},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17246},
eprint = {2609.17246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17246},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Improved weighted bounds for the strong maximal function
AU - Sheldy Ombrosi
AU - Guillermo Rey
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17246
UR - https://arxiv.org/abs/2609.17246
AB - 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 <∞ and every dimension d ≥ 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.
ER -