取消对尖锐界的超压缩证明
A hypercontractive proof of the sharp bound for cancellative pairs
- School of Statistics and Data Science, Nankai University（南开大学统计与数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文用傅里叶分析和Lifshitz算子的近L^1超压缩估计，给出了取消对尖锐界$|\mathcal{A}|\cdot|\mathcal{B}|\leq(\frac{9}{4})^n$的新证明。
AI中文摘要：
Fang和Huang证明了$[n]$的子集族$(\mathcal{A},\mathcal{B})$的每个取消对满足$|\mathcal{A}|\cdot|\mathcal{B}|\leq(\frac{9}{4})^n$。他们的证明使用了熵。我们给出一个基于Lifshitz的单侧噪声算子$\mathrm{T}^{1/4\to1/2}$的傅里叶分析证明。主要工具是该算子的近$L^1$超压缩估计。
英文摘要：
Fang and Huang proved that every cancellative pair $(\mathcal{A},\mathcal{B})$ of families of subsets of $[n]$ satisfies $|\mathcal{A}|\cdot|\mathcal{B}|\leq(\frac{9}{4})^n$. Their proof uses entropy. We give a Fourier-analytic proof based on Lifshitz's one-sided noise operator $\mathrm{T}^{1/4\to1/2}$. The main tool is a near-$L^1$ hypercontractive estimate for this operator.
