JournalsrmiVol. 28, No. 1pp. 157–178

Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields

  • Doowon Koh

    Chungbuk National University, Cheongju, South Korea
  • Chun-Yen Shen

    National Central University, Jhongli City, Taoyuan County, Taiwan
Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields cover
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Abstract

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 LpL^p-LrL^r extension estimates hold. Our main result can be considered as a nice generalization of works by Mockenhaupt and Tao in [17] and Iosevich and Koh in [10]. As an application of our sharp extension estimates, we also study the Falconer distance problems in two dimensions.

Cite this article

Doowon Koh, Chun-Yen Shen, Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields. Rev. Mat. Iberoam. 28 (2012), no. 1, pp. 157–178

DOI 10.4171/RMI/672