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arXiv · 1710.08962

Some characterizations of the preimage of $A_{\infty}$ for the Hardy-Littlewood maximal operator and consequences

Álvaro Corvalán
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Abstract

The purpose of this paper is to give some characterizations of the weight functions $w$ such that $Mw$ is in $A_{\infty}$. We show that for those weights to be in $A_{\infty}$ ensures to be in $A_{1}$. 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 $A_{1}$ but using functions of the form $(f^{\#})^δ$ and $(m_λu)^δ$ instead of $(Mf)^δ$.

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Álvaro Corvalán. 2017-11-03. Some characterizations of the preimage of $A_{\infty}$ for the Hardy-Littlewood maximal operator and consequences. https://arxiv.org/abs/1710.08962

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