Mathematics – Classical Analysis and ODEs
Scientific paper
2010-03-22
Mathematics
Classical Analysis and ODEs
18 pages. Revised version incorporates the referee's report
Scientific paper
In this paper we study extension theorems associated with general varieties in two dimensional vector spaces over finite fields. Applying Bezout's theorem, we obtain the sufficient and necessary conditions on general curves where sharp $L^p-L^r$ extension estimates hold. Our main result can be considered as a nice generalization of works by Mochenhaupt and Tao and Iosevich and Koh. As an application of our sharp extension estimates, we also study the Falconer distance problems in two dimensions.
Koh Doowon
Shen Chun-Yen
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