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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Fourier restriction and the Newton polygon
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by Ákos Magyar PDF
Proc. Amer. Math. Soc. 137 (2009), 615-625 Request permission

Abstract:

Local $L^p\to L^2$ bounds are proved for the restriction of the Fourier transform to analytic surfaces of the form $S=(x,f(x))$ in $\mathbb {R}^3$. It is found that the range of exponents is determined by the so-called distance of the Newton polygon, associated to $f$, except when the principal quasi-homogeneous part of $f(x)$ contains a factor of high multiplicity. The proofs are based on the method of Phong-Stein and Rychkov, adapted to scalar oscillatory integrals.
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Additional Information
  • Ákos Magyar
  • Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
  • Address at time of publication: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Room 121, Vancouver, British Columbia V6T 1Z2, Canada
  • MR Author ID: 318009
  • Email: amagyar2000@yahoo.com
  • Received by editor(s): August 20, 2007
  • Received by editor(s) in revised form: January 25, 2008
  • Published electronically: August 26, 2008
  • Additional Notes: This research was supported in part by NSF Grant DMS-0456490
  • Communicated by: Andreas Seeger
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 615-625
  • MSC (2000): Primary 42B10; Secondary 43A32
  • DOI: https://doi.org/10.1090/S0002-9939-08-09510-5
  • MathSciNet review: 2448583