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A restriction estimate using polynomial partitioning


Author: Larry Guth
Journal: J. Amer. Math. Soc. 29 (2016), 371-413
MSC (2010): Primary 42B20
DOI: https://doi.org/10.1090/jams827
Published electronically: May 11, 2015
MathSciNet review: 3454378
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Abstract: If $S$ is a smooth compact surface in $\mathbb {R}^3$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3.25$, $\| E_S f\|_{L^p(\mathbb {R}^3)} \le C(p,S) \| f \|_{L^\infty (S)}$. The proof uses polynomial partitioning arguments from incidence geometry.


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Additional Information

Larry Guth
Affiliation: Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
MR Author ID: 786046
Email: lguth@math.mit.edu

Received by editor(s): July 14, 2014
Received by editor(s) in revised form: January 23, 2015
Published electronically: May 11, 2015
Additional Notes: The author is supported by a Simons Investigator Award.
Article copyright: © Copyright 2015 American Mathematical Society