On the sharpness of some quantitative Muckenhoupt–Wheeden inequalities

Andrei K. Lerner; Kangwei Li; Sheldy Ombrosi; Israel P. Rivera-Ríos

doi:10.5802/crmath.638

On the sharpness of some quantitative Muckenhoupt–Wheeden inequalities

Andrei K. Lerner, Kangwei Li, Sheldy Ombrosi, Israel P. Rivera-Ríos

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In the recent work [Cruz-Uribe et al. (2021)] it was obtained that (Formular Presented) 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.

Original language	English
Pages (from-to)	1253-1260
Number of pages	8
Journal	Comptes Rendus Mathematique
Volume	362
DOIs	https://doi.org/10.5802/crmath.638
State	Published - 2024

Bibliographical note

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© 2024 Academie des sciences. All rights reserved.

Keywords

endpoint estimates
Matrix weights
quantitative bounds

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10.5802/crmath.638

Cite this

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ER -

On the sharpness of some quantitative Muckenhoupt–Wheeden inequalities

Abstract

Bibliographical note

Keywords

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