Maximal averages along a planar vector field depending on one variable
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- by Michael Bateman PDF
- Trans. Amer. Math. Soc. 365 (2013), 4063-4079 Request permission
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.References
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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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 4063-4079
- MSC (2010): Primary 42B25; Secondary 42B20
- DOI: https://doi.org/10.1090/S0002-9947-2013-05673-5
- MathSciNet review: 3055689