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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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A restriction estimate using polynomial partitioning
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by Larry Guth PDF
J. Amer. Math. Soc. 29 (2016), 371-413 Request permission

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.
  • © Copyright 2015 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 29 (2016), 371-413
  • MSC (2010): Primary 42B20
  • DOI: https://doi.org/10.1090/jams827
  • MathSciNet review: 3454378