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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Correction to ``Optimal factorization of Muckenhoupt weights''


Author: Michael Brian Korey
Journal: Trans. Amer. Math. Soc. 353 (2001), 839-851
MSC (1991): Primary 42B25; Secondary 26D15, 46E30
Published electronically: October 26, 2000
Original Article: Trans. Amer. Math. Soc. 352 (2000), 5251-5262.
MathSciNet review: 1806041
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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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Additional Information

Michael Brian Korey
Affiliation: Institut für Mathematik, Universität Potsdam, 14415 Potsdam, Germany
Email: mike@math.uni-potsdam.de

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02789-6
PII: S 0002-9947(00)02789-6
Keywords: Jones' factorization theorem, bounded mean oscillation, vanishing mean oscillation, $A_p$ condition.
Received by editor(s): February 3, 1999
Published electronically: October 26, 2000
Article copyright: © Copyright 2000 American Mathematical Society