Restriction operators acting on radial functions on vector spaces over finite fields

2012/12/20 by Doowon Koh, Koh, Doowon
Mathematics · #42B05 #43A15 #43A32 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AP #math.CA #msc:42B05 #msc:43A15 #msc:43A32

paper · pdf · doi:10.48550/arxiv.1212.5298

10 pages, no figure

arxiv created 2012/12/20 · arxiv updated 2012/12/24

Abstract

We stduy L^p-L^r restriction estimates for algebraic varieties V in the case when restriction operators act on radial functions in the finite field setting. We show that if the varieties V lie in odd dimensional vector spaces over finite fields, then the conjectured restriction estimates are possible for all radial test functions. In addition, it is proved that if the varieties V in even dimensions have few intersection points with the sphere of zero radius, the same conclusion as in odd dimensional case can be also obtained.

Related

• Weak version of restriction estimates for spheres and paraboloids in finite fields
• Connections between S-operators and restriction estimates for spheres over finite fields
• Restriction of averaging operators to algebraic varieties over finite fields
• An improved L² restriction theorem in finite fields
• Finite field restriction estimates based on Kakeya maximal operator estimates