发表机构
University of California, Irvine（加州大学尔湾分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明Hamming立方体上Walsh多项式的Bohnenblust--Hille常数随次数至多多项式增长，给出了维度一致的界，指数27非最优。
AI 中文摘要
我们证明了Hamming立方体上Walsh多项式的Bohnenblust--Hille常数在次数上至多以多项式速度增长。更精确地说，存在一个绝对常数$K$，使得每个次数至多为$m$的函数$f:\n{-1,1\}^{n} \to \mathbb{C}$满足 $$ \left(\sum_{|S|\le m}|\widehat f(S)|^{2m/(m+1)}\right)^{(m+1)/(2m)} \le Km^{27}\\|f\\|_\infty. $$ 该估计在维度上是一致的。指数$27$并非最优。
英文摘要
We prove that the Bohnenblust--Hille constants for Walsh polynomials on the Hamming cube grow at most polynomially in the degree. More precisely, there is an absolute constant $K$ such that every $f :\{-1,1\}^{n} \to \mathbb{C}$ of degree at most $m$ satisfies $$ \left(\sum_{|S|\le m}|\widehat f(S)|^{2m/(m+1)}\right)^{(m+1)/(2m)} \le Km^{27}\|f\|_\infty. $$ The estimate is uniform in the dimension. The exponent $27$ is not optimized.
Comments11 pages
