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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A $B_p$ condition for the strong maximal function
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by Liguang Liu and Teresa Luque PDF
Trans. Amer. Math. Soc. 366 (2014), 5707-5726 Request permission

Abstract:

A strong version of the Orlicz maximal operator is introduced and a natural $B_p$ condition for the rectangle case is defined to characterize its boundedness. This fact led us to describe a sufficient condition for the two weight inequalities of the strong maximal function in terms of power and logarithmic bumps. Results for the multilinear version of this operator and for other multi(sub)linear maximal functions associated with bases of open sets are also studied.
References
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Additional Information
  • Liguang Liu
  • Affiliation: Department of Mathematics, School of Information, Renmin University of China, Beijing 100872, People’s Republic of China
  • Email: liuliguang@ruc.edu.cn
  • Teresa Luque
  • Affiliation: Departamento De Análisis Matemático, Facultad de Matemáticas, Universidad De Sevilla, 41080 Sevilla, Spain
  • Email: tluquem@us.es
  • Received by editor(s): April 9, 2012
  • Received by editor(s) in revised form: August 18, 2012
  • Published electronically: June 10, 2014
  • Additional Notes: The first author was supported by the National Natural Science Foundation of China (Grant No. 11101425). The second author was supported by the Spanish Ministry of Science and Innovation Grant BES-2010-030264.
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 5707-5726
  • MSC (2010): Primary 42B20, 42B25; Secondary 47B38
  • DOI: https://doi.org/10.1090/S0002-9947-2014-05956-4
  • MathSciNet review: 3256181