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2019 Some Characterizations of the Preimage of \(A_{\infty }\) for the Hardy-Littlewood Maximal Operator and Consequences
Álvaro Corvalán
Real Anal. Exchange 44(1): 141-166 (2019). DOI: 10.14321/realanalexch.44.1.0141

Abstract

The purpose of this paper is to give some characterizations of the weight functions \(w\) such that \(Mw\in A_{\infty }\left( \mathbb{R}^{n}\right) \). We show that, for these \(Mw\) weights, being in \(A_{\infty }\) ensures being in \(A_{1}\). We give a criterion in terms of the local maximal functions \(% m_{\lambda }\) and we present a pair of applications, one of them similar to the Coifman-Rochberg characterization of \(A_{1}\) but using functions of the form \(\left( f^{\#}\right) ^{\delta }\) and \(\left( m_{\lambda }u\right) ^{\delta }\) instead of \(\left( Mf\right) ^{\delta }\).

Citation

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Álvaro Corvalán. "Some Characterizations of the Preimage of \(A_{\infty }\) for the Hardy-Littlewood Maximal Operator and Consequences." Real Anal. Exchange 44 (1) 141 - 166, 2019. https://doi.org/10.14321/realanalexch.44.1.0141

Information

Published: 2019
First available in Project Euclid: 27 June 2019

zbMATH: 07088968
MathSciNet: MR3951339
Digital Object Identifier: 10.14321/realanalexch.44.1.0141

Subjects:
Primary: 42B25

Rights: Copyright © 2019 Michigan State University Press

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Vol.44 • No. 1 • 2019
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