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Transactions of the American Mathematical Society

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



$ A_\infty$ estimates via extrapolation of Carleson measures and applications to divergence form elliptic operators

Authors: Steve Hofmann and José María Martell
Journal: Trans. Amer. Math. Soc. 364 (2012), 65-101
MSC (2010): Primary 42B99, 42B25, 35J25
Published electronically: August 2, 2011
MathSciNet review: 2833577
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Abstract: We revisit the ``extrapolation method'' for Carleson measures, introduced by Lewis and Murray (1995), to prove $ A_\infty$ estimates for certain caloric measures, and we present a purely real variable version of the method suitable for establishing $ A_\infty$ estimates. To illustrate the use of this technique, we then reprove a well-known result of Fefferman, Kenig, and Pipher (1991).

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Additional Information

Steve Hofmann
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211

José María Martell
Affiliation: Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13-15, E-28049 Madrid, Spain

Keywords: Carleson measures, $A_\infty$ Muckenhoupt weights, divergence form elliptic equations, harmonic measure.
Received by editor(s): November 23, 2009
Published electronically: August 2, 2011
Additional Notes: The first author was supported by NSF grants DMS-0245401 and DMS-0801079.
The second author was supported by MEC Grant MTM2010-16518 and by CSIC PIE 200850I015. This work has been possible thanks to the support and hospitality of the University of Missouri-Columbia (USA), the Universidad Autónoma de Madrid (Spain), the Centre de Recerca Matemàtica (Spain), the Consejo Superior de Investigaciones Científicas (Spain), and the BIRS Centre in Banff (Canada). Both authors would like to express their gratitude to these institutions.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.