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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A convolution estimate
for a measure on a curve in ${\mathbb {R}}^{4}$


Author: Daniel M. Oberlin
Journal: Proc. Amer. Math. Soc. 125 (1997), 1355-1361
MSC (1991): Primary 42B15, 42B20
MathSciNet review: 1363436
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Abstract: Let $\gamma (t)=(t,t^{2},t^{3},t^{4})$ and fix an interval $I\subset {\mathbb {R}}$. If $T$ is the operator on ${\mathbb {R}}^{4}$ defined by $Tf(x)=\int \nolimits _{I}f(x-\gamma (t))\,dt$, then $T$ maps $L^{\frac {5}{3}}({\mathbb {R}}^{4})$ into $L^{2}({\mathbb {R}}^{4})$.


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Additional Information

Daniel M. Oberlin
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-3027
Email: oberlin@math.fsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03716-7
PII: S 0002-9939(97)03716-7
Received by editor(s): July 18, 1995
Received by editor(s) in revised form: October 31, 1995
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1997 American Mathematical Society