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A new quantitative two weight theorem for the Hardy-Littlewood maximal operator


Authors: Carlos Pérez and Ezequiel Rela
Journal: Proc. Amer. Math. Soc. 143 (2015), 641-655
MSC (2010): Primary 42B25; Secondary 43A85
DOI: https://doi.org/10.1090/S0002-9939-2014-12353-7
Published electronically: October 22, 2014
MathSciNet review: 3283651
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Abstract: A quantitative two weight theorem for the Hardy-Littlewood maximal operator is proved, improving the known ones. As a consequence, a new proof of the main results in papers by Hytönen and the first author and Hytönen, the first author and Rela is obtained which avoids the use of the sharp quantitative reverse Holder inequality for $ A_{\infty }$ proved in those papers. Our results are valid within the context of spaces of homogeneous type without imposing the non-empty annuli condition.


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Carlos Pérez
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain
Email: carlosperez@us.es

Ezequiel Rela
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain
Email: erela@us.es

DOI: https://doi.org/10.1090/S0002-9939-2014-12353-7
Keywords: Two weight theorem, space of homogeneous type, Muckenhoupt weights, Calder\'on-Zygmund, maximal functions
Received by editor(s): April 26, 2013
Published electronically: October 22, 2014
Additional Notes: Both authors were supported by the Spanish Ministry of Science and Innovation grant MTM2012-30748 and by the Junta de Andalucía, grant FQM-4745.
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.