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arXiv · 1312.1742

$A_1$ weights on $\R$, an alternative approach

Eleftherios N. Nikolidakis
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Abstract

We will prove that if $ϕ$ belongs to the class $A_1(\R)$ with constant $c\ge1$ then the decreasing rearrangement of $ϕ$, belongs to the same class with constant not more than $c$. We also find for such $ϕ$ the exact best possible range of those $p>1$ for which $ϕ\in L^p$. In this way we provide alternative proofs of the results that appear in \cite{1}.

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Eleftherios N. Nikolidakis. 2014-03-30. $A_1$ weights on $\R$, an alternative approach. https://arxiv.org/abs/1312.1742

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