On the sharp upper bound related to the weak Muckenhoupt-Wheeden conjecture

Andrei K. Lerner; Fedor Nazarov; Sheldy Ombrosi

doi:10.2140/apde.2020.13.1939

On the sharp upper bound related to the weak Muckenhoupt-Wheeden conjecture

Andrei K. Lerner, Fedor Nazarov, Sheldy Ombrosi

Department of Mathematics

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

10 Scopus citations

Abstract

We construct an example showing that the upper bound [w]_A1 log(e+[w]_A1) for the L¹(w) → L1,∞(w) norm of the Hilbert transform cannot be improved in general.

Original language	English
Pages (from-to)	1939-1954
Number of pages	16
Journal	Analysis and PDE
Volume	13
Issue number	6
DOIs	https://doi.org/10.2140/apde.2020.13.1939
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020 Mathematical Sciences Publishers.

Funding

Lerner is supported by ISF grant No. 447/16 and ERC Starting Grant No. 713927, Nazarov is supported by U.S. National Science Foundation grant DMS-1600239, Ombrosi is supported by CONICET PIP 11220130100329CO, Argentina. MSC2010: 42B20, 42B25. Keywords: Hilbert transform, maximal operator, weighted inequalities.

Funders	Funder number
U.S. National Science Foundation	DMS-1600239
Horizon 2020 Framework Programme	713927
European Commission
Consejo Nacional de Investigaciones Científicas y Técnicas	PIP 11220130100329CO, MSC2010
Israel Science Foundation	447/16

Keywords

Hilbert transform
Maximal operator
Weighted inequalities

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10.2140/apde.2020.13.1939

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abstract = "We construct an example showing that the upper bound [w]A1 log(e+[w]A1) for the L1(w) → L1,∞(w) norm of the Hilbert transform cannot be improved in general.",

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KW - Weighted inequalities

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On the sharp upper bound related to the weak Muckenhoupt-Wheeden conjecture

Abstract

Bibliographical note

Funding

Keywords

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