Vol. 13, No. 6, 2020

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

Andrei K. Lerner, Fedor Nazarov and Sheldy Ombrosi

Vol. 13 (2020), No. 6, 1939–1954
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
Mathematical Subject Classification 2010
Primary: 42B20, 42B25
Milestones
Received: 21 May 2019
Accepted: 29 June 2019
Published: 12 September 2020
Authors
Andrei K. Lerner
Department of Mathematics
Bar-Ilan University
Ramat Gan
Israel
Fedor Nazarov
Department of Mathematics
Kent State University
Kent, OH
United States
Sheldy Ombrosi
Departamento de Matemática
Universidad Nacional del Sur
Bahía Blanca
Argentina