Connections between S-operators and restriction estimates for spheres over finite fields

2025/02/17 by Hunseok Kang, Kang, Hunseok, Doowon Koh +1
Computer Science · Mathematics · #42B05 #43A15 #43A32 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2502.12294

openalex publication_date 2025/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a new operator, S, which is closely related to the restriction problem for spheres in \mathbbF_q^d, the d-dimensional vector space over the finite field \mathbbF_q with q elements. The S operator is considered as a specific operator that maps functions on \mathbbF_q^d to functions on \mathbbF_q^d+1. We explore a relationship between the boundedness of the S operator and the restriction estimate for spheres in \mathbbF_q^d. Consequently, using this relationship, we prove that the L² restriction conjectures for spheres hold in all dimensions when the test functions are restricted to homogeneous functions of degree zero.

Related

• Weak version of restriction estimates for spheres and paraboloids in finite fields
• Restriction operators acting on radial functions on vector spaces over finite fields
• Extension Theorems for Spheres in the Finite Field Setting
• An improved L² restriction theorem in finite fields
• Finite field restriction estimates based on Kakeya maximal operator estimates