2026-06-01T04:21:22Zhttps://riuma.uma.es/rest/oai/requestoai:riuma.uma.es:10630/355692026-02-03T11:09:24Zcom_10630_2254col_10630_37953
RIUMA. Repositorio Institucional de la Universidad de Málaga
author
Lerner, Andrei
author
Li, Kangwei
author
Ombrosi, Sheldy J.
author
Rivera Ríos, Israel P.
2024-12-11T07:30:33Z
2024-12-11T07:30:33Z
2024
Andrei K. Lerner; Kangwei Li; Sheldy Ombrosi; Israel P. Rivera-Ríos. On the sharpness of some quantitative Muckenhoupt–Wheeden inequalities. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1253-1260. doi : 10.5802/crmath.638. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.638/
https://hdl.handle.net/10630/35569
10.5802/crmath.638
. In the recent work [Cruz-Uribe et al. (2021)] it was obtained that
|{x ∈ R
d
: w(x)|G(f w−1
)(x)| > α}| ≲
[w]
2
A1
α
Z
Rd
|f |dx
both in the matrix and scalar settings, where G is either the Hardy–Littlewood maximal function or any
Calderón–Zygmund operator. In this note we show that the quadratic dependence on [w]A1
is sharp. This
is done by constructing a sequence of scalar-valued weights with blowing up characteristics so that the
corresponding bounds for the Hilbert transform and maximal function are exactly quadratic.
eng
Attribution 4.0 Internacional
Desigualdades (Matemáticas)
On the sharpness of some quantitative Muckenhoupt-Wheeden inequalities.
journal article
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