1. CMB Online first
|Restriction Operators Acting on Radial Functions on Vector Spaces Over Finite Fields|
We study $L^p-L^r$ 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, assuming that the varieties $V$ are defined in even dimensional spaces and have few intersection points with the sphere of zero radius, we also obtain the conjectured exponents for all radial test functions.
Keywords:finite fields, radial functions, restriction operators
Categories:42B05, 43A32, 43A15