Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information


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 [Enhancements On Off] (What's this?)

  • 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 $A_p$ 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 $A_p$ 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 $A_p$ 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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 42B25, 26D15, 46E30

Retrieve articles in all journals with MSC (1991): 42B25, 26D15, 46E30

Additional Information

Michael Brian Korey
Affiliation: Institut für Mathematik, Universität Potsdam, 14415 Potsdam, Germany

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

American Mathematical Society