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

Lerner, Andrei K.; Nazarov, Fedor; Ombrosi, Sheldy

doi:10.2140/apde.2020.13.1939

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1948-206X (e-only)

ISSN: 2157-5045 (print)

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

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

DOI: 10.2140/apde.2020.13.1939

Abstract

We construct an example showing that the upper bound ${[w]}_{A_{1}} log (e + {[w]}_{A_{1}})$ for the $L^{1} (w) \to L^{1, \infty} (w)$ norm of the Hilbert transform cannot be improved in general.

PDF Access Denied

We have not been able to recognize your IP address 3.145.163.58 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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

Vol. 13, No. 6, 2020