On Fourier restriction and the Newton polygon
Author:
Ákos Magyar
Journal:
Proc. Amer. Math. Soc. 137 (2009), 615625
MSC (2000):
Primary 42B10; Secondary 43A32
Published electronically:
August 26, 2008
MathSciNet review:
2448583
Fulltext PDF Free Access
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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 socalled distance of the Newton polygon, associated to , except when the principal quasihomogeneous part of contains a factor of high multiplicity. The proofs are based on the method of PhongStein and Rychkov, adapted to scalar oscillatory integrals.
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 V.S. Rychkov: Sharp bounds for oscillatory integral operators with phases, Math. Z. 236 (2001), no. 3, 461489. MR 1821301 (2002i:42016)
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 E.M. Stein: Harmonic Analysis: RealVariable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press (1993). MR 1232192 (95c:42002)
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 H. Schulz: On the decay of the Fourier transform of measures on hypersurfaces, generated by radial functions, and related restriction theorems (unpublished).
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 P. Tomas: A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975), 477478. MR 0358216 (50:10681)
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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/S0002993908095105
PII:
S 00029939(08)095105
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 DMS0456490
Communicated by:
Andreas Seeger
Article copyright:
© Copyright 2008
American Mathematical Society
