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Restriction Operators Acting on Radial Functions on Vector Spaces over Finite Fields
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 4 / 01 December 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 834-844
- Print publication:
- 01 December 2014
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- Article
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We study
${{L}^{p}}\to {{L}^{r}}$ 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.
