On Fourier restriction and the Newton polygon

Author:
Ákos Magyar

Journal:
Proc. Amer. Math. Soc. **137** (2009), 615-625

MSC (2000):
Primary 42B10; Secondary 43A32

Published electronically:
August 26, 2008

MathSciNet review:
2448583

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Abstract | References | Similar Articles | Additional Information

Abstract: Local bounds are proved for the restriction of the Fourier transform to analytic surfaces of the form in . It is found that the range of exponents is determined by the so-called distance of the Newton polygon, associated to , except when the principal quasi-homogeneous part of 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

Email:
amagyar2000@yahoo.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09510-5

Keywords:
Fourier transform,
oscillatory integrals,
Newton polygon

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

Article copyright:
© Copyright 2008
American Mathematical Society