Some characterizations of the preimage of A_∞ for the Hardy-Littlewood maximal operator and consequences

2017/10/24 by Álvaro Corvalán, Corvalán, Álvaro
Mathematics · #26A33 #42B25 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1710.08962

openalex publication_date 2017/10/24 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to give some characterizations of the weight functions w such that Mw is in A_∞. We show that for those weights to be in A_∞ ensures to be in A₁. We give a criterion in terms of the local maximal functions m_λ and we present a pair of applications, among them someone similar to the Coifman-Rochberg characterization of A₁ but using functions of the form (f^#)^δ and (m_λu)^δ instead of (Mf)^δ.

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