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

Bar-Ilan University

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

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

Keywords

Hilbert transform
Maximal operator
Weighted inequalities

All Science Journal Classification (ASJC) codes

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2020.13.1939

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title = "On the sharp upper bound related to the weak Muckenhoupt-Wheeden conjecture",

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.",

keywords = "Hilbert transform, Maximal operator, Weighted inequalities",

author = "Lerner, {Andrei K.} and Fedor Nazarov and Sheldy Ombrosi",

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year = "2020",

doi = "10.2140/apde.2020.13.1939",

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AU - Lerner, Andrei K.

AU - Nazarov, Fedor

AU - Ombrosi, Sheldy

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Y1 - 2020

N2 - 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.

AB - 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.

KW - Hilbert transform

KW - Maximal operator

KW - Weighted inequalities

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U2 - 10.2140/apde.2020.13.1939

DO - 10.2140/apde.2020.13.1939

M3 - مقالة

SN - 2157-5045

VL - 13

SP - 1939

EP - 1954

JO - Analysis and PDE

JF - Analysis and PDE

IS - 6

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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