Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields
Journal
Revista Matematica Iberoamericana
Journal Volume
28
Journal Issue
1
Pages
157-178
Date Issued
2012
Author(s)
Koh, D.
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 Lp-Lr 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. © European Mathematical Society.
Type
journal article