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A convolution estimate for a measure on a curve in $\mathbb R^4$. II

Author(s): Daniel M. Oberlin
Journal: Proc. Amer. Math. Soc. 127 (1999), 217-221.
MSC (1991): Primary 42B15
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Abstract: This paper contains almost-sharp $L^p-L^q$ convolution estimates for measures on the curve $(t,t^2,t^3,t^4)$ in $\mathbb R^4$.

References:

[C1]
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

[C2]
M. Christ, Convolution, Curvature and Combinatorics, a Case Study, preprint.

[GSW]
A. Greenleaf, A. Seeger, and S. Wainger, On x-ray transforms for rigid line complexes and integrals over curves in $\mathbb R^4$, preprint.

[O1]
D. Oberlin, A convolution estimate for a measure on a curve in $\mathbb R^4$, Proc. Amer. Math. Soc. 125 (1997), 1355-1361. MR 97g:42009

[O2]
D. Oberlin, Multilinear proofs for two theorems on circular averages, Colloq. Math. 63 (1992), 187-190. MR 93m:42005

[O3]
D. Oberlin, Oscillatory integrals with polynomial phase, Math. Scand. 69 (1991), 45-56.

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Additional Information:

Daniel M. Oberlin
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510

DOI: 10.1090/S0002-9939-99-04690-0
PII: S 0002-9939(99)04690-0
Received by editor(s): May 12, 1997
Additional Notes: The author was partially supported by a grant from the National Science Foundation
Communicated by: Christopher D. Sogge
Copyright of article: Copyright 1999, American Mathematical Society

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