Optimal factorization of Muckenhoupt weights

Korey, Michael

doi:10.1090/S0002-9947-00-02547-2

Optimal factorization of Muckenhoupt weights
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by Michael Brian Korey PDF

Trans. Amer. Math. Soc. 352 (2000), 5251-5262 Request permission

Correction: Trans. Amer. Math. Soc. 353 (2001), 839-851.

Abstract:

Peter Jones’ theorem on the factorization of $A_p$ weights is sharpened for weights with bounds near $1$, allowing the factorization to be performed continuously near the limiting, unweighted case. When $1<p<\infty$ and $w$ is an $A_p$ weight with bound $A_p(w)=1+\varepsilon$, it is shown that there exist $A_1$ weights $u,v$ such that both the formula $w=uv^{1-p}$ and the estimates $A_1(u), A_1(v)=1+\mathcal O(\sqrt \varepsilon )$ hold. The square root in these estimates is also proven to be the correct asymptotic power as $\varepsilon \to 0$.

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