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# Restriction Operators Acting on Radial Functions on Vector Spaces Over Finite Fields

Published:2014-05-07
Printed: Dec 2014
• Doowon Koh,
Department of Mathematics, Chungbuk National University, Cheongju city, Chungbuk-Do 361-763 Korea
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## Abstract

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.
 Keywords: finite fields, radial functions, restriction operators
 MSC Classifications: 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.