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

DOI:
https://doi.org/10.1090/S0002-9947-00-02789-6

Published electronically:
October 26, 2000

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

MathSciNet review:
1806041

Full-text PDF

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 .

**1.**R. R. Coifman and C. Fefferman,*Weighted norm inequalities for maximal functions and singular integrals*, Studia Math.**51**(1974), 241-250. MR**50:10670****2.**R. R. Coifman, J. Rubio de Francia, and P. Jones,*Constructive decomposition of BMO functions and factorization of**weights*, Proc. Amer. Math. Soc.**87**(1983), 675-676. MR**84c:42031****3.**J. García-Cuerva and J. L. Rubio de Francia,*Weighted norm inequalities and related topics*, North-Holland, Amsterdam, New York, and Oxford, 1985. MR**87d:42043****4.**J. Garnett and P. Jones,*BMO from dyadic BMO*, Pacific J. Math.**99**(1982), 351-371. MR**85d:42021****5.**P. J. Holden,*Extension theorems for functions of vanishing mean oscillation*, Pacific J. Math.**142**(1990), 277-295. MR**91c:42027****6.**P. Jones,*Factorization of**weights*, Ann. of Math.**111**(1980), 511-530. MR**82b:46035****7.**F. John and L. Nirenberg,*On functions of bounded mean oscillation*, Comm. Pure Appl. Math.**14**(1961), 415-426. MR**24:A1348****8.**M. B. Korey,*Ideal weights: doubling and absolute continuity with asymptotically optimal bounds*, Ph.D. Thesis, University of Chicago, 1995.**9.**M. B. Korey,*Ideal weights: asymptotically optimal versions of doubling, absolute continuity, and mean oscillation*, J. Fourier Anal. Appl.**4**(1998), 491-519. CMP**99:05****10.**B. Muckenhoupt,*Weighted norm inequalities for the Hardy maximal function*, Trans. Amer. Math. Soc.**165**(1972), 207-226. MR**45:2461****11.**A. Politis,*Sharp results on the relation between weight spaces and BMO*, Ph.D. Thesis, University of Chicago, 1995.**12.**J. Rubio de Francia,*Factorization and extrapolation of weights*, Bull. Amer. Math. Soc.**7**(1982), 393-395. MR**83i:42016****13.**J. Rubio de Francia,*Factorization theory and**weights*, Amer. J. Math.**106**(1984), 533-547. MR**86a:47028a****14.**W. Rudin,*Functional analysis*, McGraw-Hill, New York, 1973. MR**51:1315****15.**E. M. Stein,*Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals*, Princeton Univ. Press, Princeton, NJ, 1993. MR**95c:42002****16.**K. Yosida,*Functional analysis*, Grundlehren Math. Wiss., vol. 123, Springer-Verlag, Berlin, Heidelberg, and New York, 1965. MR**31:5054**

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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:
https://doi.org/10.1090/S0002-9947-00-02789-6

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