Proceedings of the American Mathematical Society

Author(s): Daniel M. Oberlin
Journal: Proc. Amer. Math. Soc. 132 (2004), 3195-3201.
MSC (2000): Primary 42B20
Posted: June 16, 2004
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Abstract: We obtain a Fourier transform estimate and an $L^{3/2}({\mathbb{R}}^{2}) -L^{3}({\mathbb{R}}^{2})$ convolution estimate for certain measures on a class of convex curves in the plane.

1.: Y. Choi, Convolution operators with affine arclength measures on plane curves, J. Korean Math. Soc. 36 (1999), 193-207. MR 2000a:42021
2.: 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 87b:42018
3.: S.W. Drury, Degenerate curves and harmonic analysis, Math. Proc. Camb. Phil. Soc. 108 (1990), 89-96. MR 91h:42021
4.: S. W. Drury and K. Guo, Convolution estimates related to surfaces of half the ambient dimension, Math. Proc. Camb. Phil. Soc. 110 (1991), 151-159. MR 92j:42012
5.: W. Littman, $L^{p} -L^{q}$ estimates for singular integral operators, Proc. Sympos. Pure Math. 23 (1971), 479-481. MR 50:10909
6.: D.M. Oberlin, Oscillatory integrals with polynomial phase, Math. Scand. 69 (1991), 45-56. MR 93c:41048
7.: -, Convolution with affine arclength measures in the plane, Proc. Amer. Math. Soc. 127 (1999), 3591-3592. MR 2000c:42016
8.: -, Fourier restriction for affine arclength measures in the plane, Proc. Amer. Math. Soc. 129 (2001), 3303-3305. MR 2002g:42013
9.: P. Sjölin, Fourier multipliers and estimates of the Fourier transform carried by smooth curves in $\mathbb{R} ^{2}$ , Studia Math. 51 (1974), 169-182. MR 52:6299

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B20

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

DOI: 10.1090/S0002-9939-04-07610-5
PII: S 0002-9939(04)07610-5
Keywords: Fourier transform, convolution
Received by editor(s): March 27, 2002
Posted: June 16, 2004
Additional Notes: The author was partially supported by a grant from the National Science Foundation
Communicated by: Andreas Seeger
Copyright of article: Copyright 2004, American Mathematical Society

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