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$ L^{p}$ boundedness of maximal averages over hypersurfaces in $ \mathbb{R}^{3}$


Author: Michael Greenblatt
Journal: Trans. Amer. Math. Soc. 365 (2013), 1875-1900
MSC (2010): Primary 42B20
DOI: https://doi.org/10.1090/S0002-9947-2012-05697-2
Published electronically: September 19, 2012
MathSciNet review: 3009647
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Abstract: Extending the methods developed in the author's recent paper and using some techniques from a paper by Sogge and Stein in conjunction with various facts about adapted coordinate systems in two variables, an $ L^p$ boundedness theorem is proven for maximal operators over hypersurfaces in $ \mathbb{R}^3$ when $ p > 2.$ When the best possible $ p$ is greater than $ 2$, the theorem typically provides sharp estimates. This gives another approach to the subject of recent work of Ikromov, Kempe, and Müller (2010).


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Additional Information

Michael Greenblatt
Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices, 851 S. Morgan Street, Chicago, Illinois 60607-7045

DOI: https://doi.org/10.1090/S0002-9947-2012-05697-2
Received by editor(s): April 27, 2011
Published electronically: September 19, 2012
Additional Notes: This research was supported in part by NSF grant DMS-0919713
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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