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

   

 

Maximal averages along a planar vector field depending on one variable


Author: Michael Bateman
Journal: Trans. Amer. Math. Soc. 365 (2013), 4063-4079
MSC (2010): Primary 42B25; Secondary 42B20
Published electronically: March 12, 2013
MathSciNet review: 3055689
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove (essentially) sharp $ L^2$ estimates for a restricted maximal operator associated to a planar vector field that depends only on the horizontal variable. The proof combines an understanding of such vector fields from earlier work of the author with a result of Nets Katz on directional maximal operators.


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Additional Information

Michael Bateman
Affiliation: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, California 90095-1555
Address at time of publication: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom
Email: bateman@math.ucla.edu, m.bateman@dpmms.com.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05673-5
Received by editor(s): June 20, 2011
Received by editor(s) in revised form: July 15, 2011
Published electronically: March 12, 2013
Additional Notes: This work was supported by NSF grant DMS-0902490
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.