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

DOI10.4153/CMB-2014-016-2zbMath1307.43001arXiv1212.5298OpenAlexW2963047777MaRDI QIDQ2933765

Doowon Koh

Publication date: 5 December 2014

Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1212.5298

zbMATH Keywords

finite fieldsradial functionsrestriction operators

Mathematics Subject Classification ID

Fourier series and coefficients in several variables (42B05) Other transforms and operators of Fourier type (43A32) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items (3)

New restriction estimates for the 3-d paraboloid over finite fields ⋮ Weak version of restriction estimates for spheres and paraboloids in finite fields ⋮ Finite field restriction estimates based on Kakeya maximal operator estimates

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