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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Optimal factorization of Muckenhoupt weights
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by Michael Brian Korey
Trans. Amer. Math. Soc. 352 (2000), 5251-5262
DOI: https://doi.org/10.1090/S0002-9947-00-02547-2
Published electronically: July 18, 2000

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 $\varepsilon \to 0$.
References
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Bibliographic Information
  • Michael Brian Korey
  • Affiliation: Institut für Mathematik, Universität Potsdam, 14415 Potsdam, Germany
  • Email: mike@math.uni-potsdam.de
  • Received by editor(s): February 3, 1999
  • Published electronically: July 18, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 5251-5262
  • MSC (1991): Primary 42B25; Secondary 26D15, 46E30
  • DOI: https://doi.org/10.1090/S0002-9947-00-02547-2
  • MathSciNet review: 1694375