Averaging Operators Over Homogeneous Varieties Over Finite Fields

Doowon Koh, Chun Yen Shen*, Igor Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)1415-1441
Number of pages27
JournalJournal of Geometric Analysis
Volume26
Issue number2
DOIs
Publication statusPublished - 1 Apr 2016
Externally publishedYes

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