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

   

 

Asymptotical stability of Muckenhoupt weights through Gurov-Reshetnyak classes


Authors: Daniel Aalto and Lauri Berkovits
Journal: Trans. Amer. Math. Soc. 364 (2012), 6671-6687
MSC (2010): Primary 42B25, 30L99
Published electronically: June 12, 2012
MathSciNet review: 2958951
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Abstract: We show that weights in the Gurov-Reshetnyak class $ GR_\varepsilon (\mu )$ satisfy a weak reverse Hölder inequality with an explicit and asymptotically sharp bound for the exponent, thus extending classical results from the Euclidean setting to doubling metric measure spaces. As an application, we study asymptotical behaviour of embeddings between Muckenhoupt classes and reverse Hölder classes.


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Additional Information

Daniel Aalto
Affiliation: Department of Signal Processing and Acoustics, Aalto University School of Electrical Engineering, FI-00076 Aalto University, Finland
Email: daniel.aalto@iki.fi

Lauri Berkovits
Affiliation: Department of Mathematics, FI-90014 University of Oulu, Finland
Email: lauri.berkovits@oulu.fi

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05677-7
Received by editor(s): May 12, 2011
Published electronically: June 12, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.