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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A new quantitative two weight theorem for the Hardy-Littlewood maximal operator
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by Carlos Pérez and Ezequiel Rela PDF
Proc. Amer. Math. Soc. 143 (2015), 641-655 Request permission

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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Additional Information
  • 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
  • MR Author ID: 887397
  • Email: erela@us.es
  • 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
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 3283651