Weak version of restriction estimates for spheres and paraboloids in finite fields

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:419

Article

Kang, Hunseok¹  Koh, Doowon² 

[1] Soongsil Univ, Dept Math, Seoul 156749, South Korea

[2] Chungbuk Natl Univ, Dept Math, Cheongju 361Z763, Chungbuk Do, South Korea

关键词: Homogeneous function;    Finite field;    Restriction operators;   

DOI  :  10.1016/j.jmaa.2014.05.028

来源: Elsevier

【 摘 要 】

We study L-P-L-T restriction estimates for algebraic varieties in d-dimensional vector spaces over finite fields. Unlike the Euclidean case, if the dimension d is even, then it is conjectured that the L(2d+2)/(d+3) - L-2 Stein-Tomas restriction result can be improved to the L(2d+4)/(d+4) - L-2 estimate for both spheres and paraboloids in finite fields. In this paper we show that the conjectured L-P - L-2 restriction estimate holds in the specific case when test functions under consideration are restricted to d-coordinate functions or homogeneous functions of degree zero. To deduce our result, we use the connection between the restriction phenomena for our varieties in d dimensions and those for homogeneous varieties in (d + 1) dimensions. (C) 2014 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license

【 授权许可】

Free