A uniform estimate for Fourier restriction to simple curves
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- by Daniel M. Oberlin PDF
- Proc. Amer. Math. Soc. 137 (2009), 4227-4242 Request permission
Abstract:
We prove a uniform Fourier extension-restriction estimate for a certain class of curves in $\mathbb {R}^d$.References
- Jong-Guk Bak, Daniel M. Oberlin, and Andreas Seeger, Restriction of Fourier transforms to curves and related oscillatory integrals, Amer. J. Math. 131 (2009), no. 2, 277–311. MR 2503984, DOI 10.1353/ajm.0.0044
- Jong-Guk Bak, Daniel M. Oberlin, and Andreas Seeger, Restriction of Fourier transforms to curves. II. Some classes with vanishing torsion, J. Aust. Math. Soc. 85 (2008), no. 1, 1–28. MR 2460861, DOI 10.1017/S1446788708000578
- Michael Christ, On the restriction of the Fourier transform to curves: endpoint results and the degenerate case, Trans. Amer. Math. Soc. 287 (1985), no. 1, 223–238. MR 766216, DOI 10.1090/S0002-9947-1985-0766216-6
- S. Dendrinos and J. Wright, Fourier restriction to polynomial curves I: a geometric inequality, preprint.
- S. W. Drury and B. P. Marshall, Fourier restriction theorems for curves with affine and Euclidean arclengths, Math. Proc. Cambridge Philos. Soc. 97 (1985), no. 1, 111–125. MR 764500, DOI 10.1017/S0305004100062654
- S. W. Drury and B. P. Marshall, Fourier restriction theorems for degenerate curves, Math. Proc. Cambridge Philos. Soc. 101 (1987), no. 3, 541–553. MR 878901, DOI 10.1017/S0305004100066901
- Daniel M. Oberlin, Fourier restriction for affine arclength measures in the plane, Proc. Amer. Math. Soc. 129 (2001), no. 11, 3303–3305. MR 1845006, DOI 10.1090/S0002-9939-01-06012-9
- Daniel M. Oberlin, Some convolution inequalities and their applications, Trans. Amer. Math. Soc. 354 (2002), no. 6, 2541–2556. MR 1885663, DOI 10.1090/S0002-9947-01-02921-X
- Per Sjölin, Fourier multipliers and estimates of the Fourier transform of measures carried by smooth curves in $R^{2}$, Studia Math. 51 (1974), 169–182. MR 385437, DOI 10.4064/sm-51-2-169-182
Additional Information
- Daniel M. Oberlin
- Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
- Email: oberlin@math.fsu.edu
- Received by editor(s): November 6, 2008
- Received by editor(s) in revised form: May 26, 2009
- Published electronically: August 4, 2009
- Additional Notes: The author was supported in part by NSF grant DMS-0552041.
- Communicated by: Michael T. Lacey
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 4227-4242
- MSC (2000): Primary 42B10
- DOI: https://doi.org/10.1090/S0002-9939-09-10047-3
- MathSciNet review: 2538584