Finite field analogue of restriction theorem for general measures

TL;DR

This paper investigates restriction problems in finite field vector spaces, establishing a finite field analogue of a known restriction theorem and demonstrating the sharpness of the exponential range.

Contribution

It introduces a finite field analogue of the Mockenhaupt-Mitsis-Bak-Seenger restriction theorem and proves the sharpness of the exponential range.

Findings

Finite field analogue of the restriction theorem established

Range of exponentials shown to be sharp

Advances understanding of restriction phenomena in finite fields

Abstract

We study restriction problem in vector spaces over finite fields. We obtain finite field analogue of Mockenhaupt-Mitsis-Bak-Seenger restriction theorem, and we show that the range of the exponentials is sharp.