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Some convolution inequalities and their applications
Author(s):
Daniel
M.
Oberlin
Journal:
Trans. Amer. Math. Soc.
354
(2002),
2541-2556.
MSC (2000):
Primary 42B10
Posted:
November 30, 2001
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Abstract:
We introduce a class of convolution inequalities and study the implications of these inequalities for certain problems in harmonic analysis.
References:
-
- 1.
- J.-G. Bak, An
 - estimate for Radon transforms associated to polynomials, Duke Math. J. 101 (2000), 259-269. MR 2001b:42012 - 2.
- J.-G. Bak, D.M. Oberlin, and A. Seeger, Two endpoint bounds for generalized Radon transforms in the plane, Revista Math. (to appear).
- 3.
- B. B. Taberner, On the restriction of the Fourier transform to a conical surface, Trans. Amer. Math. Soc. 292 (1985), 321-333. MR 86k:42023
- 4.
- M. Christ, Estimates for the
 plane transform, Indiana Univ. Math. J. 33 (1984), 891-910. MR 86k:44004 - 5.
- -, 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
- 6.
- S.W. Drury, Restrictions of Fourier transforms to curves, Ann. Inst. Fourier, Grenoble 35 (1985), 117-123. MR 86e:42026
- 7.
- -, A survey of
 plane transforms, Contemp. Math. 91 (1989), 43-55. MR 92b:44002 - 8.
- -, Degenerate curves and harmonic analysis, Math. Proc. Camb. Phil. Soc. 108 (1990), 89-96. MR 91h:42021
- 9.
- 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
- 10.
- -, Some remarks on the restriction of the Fourier transform to surfaces, Math. Proc. Camb. Phil. Soc. 113 (1993), 153-159. MR 94f:42020
- 11.
- S.W. Drury and B.P. Marshall, Fourier restriction theorems for curves with affine and Euclidean arclengths, Math. Proc. Camb. Phil. Soc. 97 (1985), 111-125. MR 87b:42019
- 12.
- J. Harmse, On Lebesgue space estimates for the wave equation, Indiana Univ. Math. J. 39 (1990), 229-248. MR 91j:35158
- 13.
- G.H. Hardy, J.E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, 1959. MR 13:727e (1952 ed.)
- 14.
- D.M. Oberlin, Convolution estimates for some distributions with singularities on the light cone, Duke Math. J. 59 (1989), 747-757. MR 91f:46053
- 15.
- -, Multilinear proofs for two theorems on circular averages, Colloq. Math. 63 (1992), 187-190. MR 93m:42005
- 16.
- -, Convolution with affine arclength measures in the plane, Proc. Amer. Math. Soc. 127 (1999), 3591-3592. MR 2000c:42016
- 17.
- -, Convolution with measure on hypersurfaces, Math. Proc. Camb. Phil. Soc. 129 (2000), 517-526. MR 2001j:42014
- 18.
- -, Convolution with measures on polynomial curves, Math. Scand. (to appear).
- 19.
- -, Fourier restriction for affine arclengthmeasures in the plane, Proc. Amer. Math. Soc. 129 (2001), 3303-3305. CMP 2001:16
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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/S0002-9947-01-02921-X
PII:
S 0002-9947(01)02921-X
Keywords:
Convolution,
restriction
Received by editor(s):
May 2, 2001
Received by editor(s) in revised form:
June 21, 2001
Posted:
November 30, 2001
Additional Notes:
The author was partially supported by the NSF
Copyright of article:
Copyright
2001,
American Mathematical Society
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