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

 

Carleson conditions for asymptotic weights


Author: Michael Brian Korey
Journal: Trans. Amer. Math. Soc. 350 (1998), 2049-2069
MSC (1991): Primary 42B25; Secondary 26D15, 31B35
MathSciNet review: 1422902
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Abstract: The doubling and $A_\infty$ conditions are characterized in terms of convolution with rapidly decreasing kernels. The Carleson-measure criterion for $A_\infty$ of Fefferman, Kenig, and Pipher is extended to the case when all bounds become optimally small in the asymptotic limit.


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Additional Information

Michael Brian Korey
Affiliation: Max-Planck-Arbeitsgruppe “Partielle Differentialgleichungen und Komplexe Analysis”, Universität Potsdam, 14415 Potsdam, Germany
Address at time of publication: Institut für Mathematik, Universität Potsdam, 14415 Potsdam, Germany
Email: mike@mpg-ana.uni-potsdam.de

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01931-X
PII: S 0002-9947(98)01931-X
Keywords: Doubling measure, vanishing mean oscillation, $A_\infty$ condition, Carleson measure.
Received by editor(s): December 28, 1995
Received by editor(s) in revised form: September 5, 1996
Additional Notes: Supported by the Max-Planck-Gesellschaft. This work is a revised form of part of the author’s dissertation, which was written under Professor Carlos E. Kenig at the University of Chicago. Another portion of the dissertation \cite{Ko} is to appear in J.\ Fourier Anal.\ Appl.
Article copyright: © Copyright 1998 American Mathematical Society