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arXiv · 1212.5298

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

Doowon Koh
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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.

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Doowon Koh. 2012-12-20. Restriction operators acting on radial functions on vector spaces over finite fields. https://arxiv.org/abs/1212.5298

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