发表机构
Indiana University（印第安纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了三维空间中抛物面条带的尖锐解耦估计，通过归约为平面关联问题并利用两端Furstenberg估计，受Wang-Wu方法启发。
AI 中文摘要
大帽或大系综解耦不等式最初由 Demeter 研究。这些不等式与傅里叶限制理论中的反向平方函数猜想和限制猜想密切相关。所谓条带，是指将抛物面的 $R^{-1}$ 邻域划分为 $1\times R^{-1/2}\times R^{-1}$ 的弯曲大帽。本文证明了 $\mathbb{R}^3$ 中条带的尖锐 $\ell^2(L^{10/3})$ 解耦估计。我们将条带解耦不等式归结为一个平面关联问题，并通过两端 Furstenberg 关联估计来处理。我们的方法受 Wang--Wu 关于限制猜想的工作启发。
英文摘要
Large-cap or large-ensemble decoupling inequalities were initially studied by Demeter. These are intimately connected to the reverse square-function conjecture and restriction conjecture in Fourier restriction theory. By strips, we mean a partition of the $R^{-1}$-neighborhood of the paraboloid into $1\times R^{-1/2}\times R^{-1}$ curved large-caps. In this article, we prove the sharp $\ell^2(L^{10/3})$ decoupling estimate for strips in $\mathbb{R}^3$. We reduce the strip decoupling inequalities to a planar incidence problem, which is dealt with via two-ends Furstenberg incidence estimates. Our method is inspired by Wang--Wu on the restriction conjecture.
Comments21 pages, 4 figures
