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Weighted inequalities for the two-dimensional one-sided Hardy-Littlewood maximal function

Authors: L. Forzani, F. J. Martín-Reyes and S. Ombrosi
Journal: Trans. Amer. Math. Soc. 363 (2011), 1699-1719
MSC (2010): Primary 42B25; Secondary 47A35, 37A40
Published electronically: November 1, 2010
MathSciNet review: 2746661
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Abstract: In this work we characterize the pairs of weights $ (w,v)$ such that the one-sided Hardy-Littlewood maximal function in dimension two is of weak-type $ (p,p)$, $ 1\leq p<\infty$, with respect to the pair $ (w,v)$. As an application of this result we obtain a generalization of the classic Dunford-Schwartz Ergodic Maximal Theorem for bi-parameter flows of null-preserving transformations.

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Additional Information

L. Forzani
Affiliation: IMAL-CONICET, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, Argentina

F. J. Martín-Reyes
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071-Málaga, Spain

S. Ombrosi
Affiliation: Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina

Keywords: Weights, one-sided maximal function, ergodic maximal theorem
Received by editor(s): May 28, 2007
Published electronically: November 1, 2010
Additional Notes: The research of the first author has been partially supported by CONICET, grant PIP 5810, and the Universidad Nacional del Litoral
The research of the second author has been partially supported by the Junta de Andalucía, grants FQM-354 and the FQM-01509, and the Spanish government, grants MTM2005-08350-C03-02 and MTM2008-06621-C02-02
The research of the third author has been partially supported by the Universidad Nacional del Sur, grant SGCyT-UNS PGI 24/L058, and by a grant of the Spanish government, MEC Res. 26/05/2006
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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