Finite field analogue of restriction theorem for general measures

Abstract:

We study Fourier transformation of functions in vector spaces over finite fields. Specially we talk about finite field analogue of restriction problem, a basic problem in harmonic analysis. G. Mockenhaupt and T. Tao initially studied the finite field analogue of restriction problem. By adapting their arguments we obtain finite field analogue of Mockenhaupt-Mitsis-Bak-Seenger restriction theorem. Furthermore, inspired by the constructions of K. Hambrook, I. Laba, X. Chen for the Euclidean setting, we show that the range of the exponentials is sharp for the finite fields setting.