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Convolution and restriction estimates for measures on curves in $ \mathbb{R}^2$

Author(s): Daniel M. Oberlin
Journal: Proc. Amer. Math. Soc. 136 (2008), 213-217.
MSC (2000): Primary 42B10
Posted: October 5, 2007
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Abstract: We study convolution and Fourier restriction estimates for some degenerate curves in $ \mathbb{R} ^2$.

References:

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J.-G. Bak, D. Oberlin, and A. Seeger, Restriction of Fourier transforms to degenerate simple curves, J. Australian Math. Soc., to appear.

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S. W. Drury, Degenerate curves and harmonic analysis, Math. Proc. Camb. Phil. Soc. 108 (1990), 89-96. MR 1049762 (91h:42021)

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D. Oberlin, Convolution with affine arclength measures in the plane, Proc. Amer. Math. Soc. 127 (1999), 3591-3592. MR 1690999 (2000c:42016)

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D. Oberlin, Fourier restriction for affine arclength measures in the plane, Proc. Amer. Math. Soc. 129 (2001), 3303-3305. MR 1845006 (2002g:42013)

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P. Sjölin, Fourier multipliers and estimates of the Fourier transform of measures carrried by smooth curves in $ \mathbb{R} ^2$, Studia Math. 51 (1974), 169-182. MR 0385437 (52:6299)

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E. M. Stein, Harmonic analysis in $ \mathbb{R} ^n$, Studies in Harmonic Analysis, MAA Studies in Mathematics 13, Mathematical Association of America, Washington, D.C., 1976. MR 0461002 (57:990)

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Additional Information:

Daniel M. Oberlin
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510
Email: oberlin@math.fsu.edu

DOI: 10.1090/S0002-9939-07-09083-1
PII: S 0002-9939(07)09083-1
Keywords: Convolution, Fourier restriction
Received by editor(s): October 16, 2006
Posted: October 5, 2007
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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