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Covering lemmas associated to maximal operators of weak type
Abstract
Building on the work of A. Córdoba and R. Fefferman, we provide a necessary and sufficient covering condition on a basis ℬ on a separable metric space X with a Borel measure μ so that the associated \mbox{geometric} maximal operator MB satisfies for all α> 0 the weak type estimate μ({x ∈ X : MBf(x) > α}) ≤ ∫XΦ( γB |f/α|) dμ , where Φ: [0, ∞) → [0, ∞) is an everywhere finite Young's function.
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BibTeX
@misc{hagelstein2026covering,
title = {{Covering lemmas associated to maximal operators of weak type}},
author = {Paul Hagelstein and Fedor Nazarov and Blanca Radillo-Murguia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30327},
eprint = {2610.30327},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30327},
}
RIS
TY - UNPB
TI - Covering lemmas associated to maximal operators of weak type
AU - Paul Hagelstein
AU - Fedor Nazarov
AU - Blanca Radillo-Murguia
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30327
UR - https://arxiv.org/abs/2610.30327
AB - Building on the work of A. Córdoba and R. Fefferman, we provide a necessary and sufficient covering condition on a basis ℬ on a separable metric space X with a Borel measure μ so that the associated \mbox{geometric} maximal operator M_B satisfies for all α> 0 the weak type estimate μ({x ∈ X : M_Bf(x) > α}) ≤ ∫_XΦ( γ_B |f/α|) dμ , where Φ: [0, ∞) → [0, ∞) is an everywhere finite Young's function.
ER -