Asymptotical stability of Muckenhoupt weights through Gurov-Reshetnyak classes
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- by Daniel Aalto and Lauri Berkovits PDF
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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.References
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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
- Received by editor(s): May 12, 2011
- Published electronically: June 12, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 6671-6687
- MSC (2010): Primary 42B25, 30L99
- DOI: https://doi.org/10.1090/S0002-9947-2012-05677-7
- MathSciNet review: 2958951