Optimal factorization of Muckenhoupt weights

Author:
Michael Brian Korey

Journal:
Trans. Amer. Math. Soc. **352** (2000), 5251-5262

MSC (1991):
Primary 42B25; Secondary 26D15, 46E30

Published electronically:
July 18, 2000

MathSciNet review:
1694375

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Abstract | References | Similar Articles | Additional Information

Peter Jones' theorem on the factorization of weights is sharpened for weights with bounds near , allowing the factorization to be performed continuously near the limiting, unweighted case. When and is an weight with bound , it is shown that there exist weights such that both the formula and the estimates hold. The square root in these estimates is also proven to be the correct asymptotic power as .

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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/S0002-9947-00-02547-2

Keywords:
Jones' factorization theorem,
bounded mean oscillation,
vanishing mean oscillation,
$A_p$ condition.

Received by editor(s):
February 3, 1999

Published electronically:
July 18, 2000

Article copyright:
© Copyright 2000
American Mathematical Society