Averaging Operators Over Homogeneous Varieties Over Finite Fields
Journal
Journal of Geometric Analysis
Journal Volume
26
Journal Issue
2
Pages
1415-1441
Date Issued
2016
Author(s)
Abstract
In this paper we study the mapping properties of the averaging operator over a variety given by a system of homogeneous equations over a finite field. We obtain optimal results on the averaging problems over two-dimensional varieties whose elements are common solutions of diagonal homogeneous equations. The proof is based on a careful study of algebraic and geometric properties of such varieties. In particular, we show that they are not contained in any hyperplane and are complete intersections. We also address partial results on averaging problems over arbitrary dimensional homogeneous varieties which are smooth away from the origin.
Type
journal article