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A uniform estimate for Fourier restriction to simple curves

Author(s): Daniel M. Oberlin
Journal: Proc. Amer. Math. Soc. 137 (2009), 4227-4242.
MSC (2000): Primary 42B10
Posted: August 4, 2009
MathSciNet review: 2538584
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Abstract | References | Similar articles | Additional information

Abstract: We prove a uniform Fourier extension-restriction estimate for a certain class of curves in $\mathbb{R}^d$ .

References:

1.: J.-G. Bak, D. Oberlin and A. Seeger, Restriction of Fourier transforms to curves and related oscillatory integrals, Amer. J. Math. 131 (2009), 277-311. MR 2503984
2.: -, Restriction of Fourier transforms to curves. II: some classes with vanishing torsion, J. Australian Math. Soc. 85 (2008), 1-28. MR 2460861
3.: M. Christ, On the restriction of the Fourier transform to curves: endpoint results and the degenerate case, Trans. Amer. Math. Soc. 287 (1985), 223-238. MR 766216 (87b:42018)
4.: S. Dendrinos and J. Wright, Fourier restriction to polynomial curves I: a geometric inequality, preprint.
5.: S.W. Drury and B. Marshall, Fourier restriction theorems for curves with affine and Euclidean arclengths, Math. Proc. Cambridge Philos. Soc. 97 (1985), 111-125. MR 764500 (87b:42019)
6.: -, Fourier restriction theorems for degenerate curves, Math. Proc. Cambridge Philos. Soc. 101 (1987), 541-553. MR 878901 (88e:42026)
7.: D. Oberlin, Fourier restriction for affine arclength measures in the plane, Proc. Amer. Math. Soc. 129 (2001), 3303-3305. MR 1845006 (2002g:42013)
8.: -, Some convolution inequalities and their applications, Trans. Amer. Math. Soc. 354 (2002), 2541-2556. MR 1885663 (2002j:42016)
9.: P. Sjölin, Fourier multipliers and estimates of the Fourier transform of measures carried by smooth curves in $R\sp{2}$ , Studia Math. 51 (1974), 169-182. MR 0385437 (52:6299)

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Additional Information:

Daniel M. Oberlin
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Email: oberlin@math.fsu.edu

DOI: 10.1090/S0002-9939-09-10047-3
PII: S 0002-9939(09)10047-3
Keywords: Fourier transforms of measures on curves, Fourier restriction problem, affine arclength measure
Received by editor(s): November 6, 2008,
Received by editor(s) in revised form: May 26, 2009
Posted: August 4, 2009
Additional Notes: The author was supported in part by NSF grant DMS-0552041.
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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