Restriction Operators Acting on Radial Functions on Vector Spaces over Finite Fields

Koh, Doowon

Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 834-844

Résumé

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.

Détail

DOI : 10.4153/CMB-2014-016-2

Mots-clés : 42B05, 43A32, 43A15, finite fields, radial functions, restriction operators.

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