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

 

A $ B_p$ condition for the strong maximal function


Authors: Liguang Liu and Teresa Luque
Journal: Trans. Amer. Math. Soc. 366 (2014), 5707-5726
MSC (2010): Primary 42B20, 42B25; Secondary 47B38
Published electronically: June 10, 2014
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05956-4
PII: S 0002-9947(2014)05956-4
Keywords: Strong maximal operators, $B_p$ condition, bump condition.
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.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.