$L^{p}$ boundedness of maximal averages over hypersurfaces in $\mathbb {R}^{3}$
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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).References
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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
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 1875-1900
- MSC (2010): Primary 42B20
- DOI: https://doi.org/10.1090/S0002-9947-2012-05697-2
- MathSciNet review: 3009647