Restriction Operators Acting on Radial Functions on Vector Spaces Over Finite Fields
Printed: Dec 2014
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.
finite fields, radial functions, restriction operators
42B05 - Fourier series and coefficients
43A32 - Other transforms and operators of Fourier type
43A15 - $L^p$-spaces and other function spaces on groups, semigroups, etc.