Extension theorems for Hamming varieties over finite fields

2019/03/10 by Cheong, Daewoong, Koh, Doowon, Pham, Thang · 2 citations
#Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.03904

Abstract

We study the finite field extension estimates for Hamming varieties H_j, j∈ \mathbb F_q^*, defined by H_j=\x∈ \mathbb F_q^d: ∏_k=1^d x_k=j\, where \mathbb F_q^d denotes the d-dimensional vector space over a finite field \mathbb F_q with q elements. We show that although the maximal Fourier decay bound on H_j away from the origin is not good, the Stein-Tomas L²→ L^r extension estimate for H_j holds.

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