PreprintarXiv licencearXiv
Polynomial Bohnenblust--Hille bounds for product of cyclic groups
Abstract
Fix an integer K≥2, and let CKn ={(e2πij/K)j=0K−1}n be the product of cyclic groups of order K. For a Fourier character χα, let s(α) be the number of active coordinates. We give a self-contained proposed proof that the dimension-free Bohnenblust--Hille constants governed by interaction order grow polynomially: if pd=2d/(d+1) and γ2=1/2, γK=(Klog(K−1))/(4(K−2)) (K≥3), then the ℓpd norm of Fourier coefficients {f̂(α)} is bounded by L∞ norm of f multiplied by C(K) d4γK+5. The constant C(K) is actually at most of the order K5/2.
Related
- Polynomial Bohnenblust--Hille Bounds and Hardy--Littlewood Inequalities for Finite Local Systems
- Extensions of a family of Linear Cycle Sets whose underlying group is a product of two cyclic groups
- Resultant of an equivariant polynomial system with respect to a direct product of r symmetric groups
- The Strong Naor--Schechtman Convolution Inequality on the Product of Cyclic Groups
- Polynomial growth of Bohnenblust--Hille constants on the Hamming cube
BibTeX
@misc{slote2026polynomial,
title = {{Polynomial Bohnenblust--Hille bounds for product of cyclic groups}},
author = {Joseph Slote and Alexander Volberg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07758},
eprint = {2609.07758},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07758},
}
RIS
TY - UNPB
TI - Polynomial Bohnenblust--Hille bounds for product of cyclic groups
AU - Joseph Slote
AU - Alexander Volberg
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.07758
UR - https://arxiv.org/abs/2609.07758
AB - Fix an integer K≥2, and let C_K^n ={(e^2πij/K)_j=0^K−1}^n be the product of cyclic groups of order K. For a Fourier character χ_α, let s(α) be the number of active coordinates. We give a self-contained proposed proof that the dimension-free Bohnenblust--Hille constants governed by interaction order grow polynomially: if p_d=2d/(d+1) and γ_2=1/2, γ_K=(Klog(K−1))/(4(K−2)) (K≥3), then the ℓ^p_d norm of Fourier coefficients {f̂(α)} is bounded by L^∞ norm of f multiplied by C(K) d^4γ_K+5. The constant C(K) is actually at most of the order K^5/2.
ER -