SHARP BOUNDS FOR MULTILINEAR CURVED KAKEYA, RESTRICTION AND OSCILLATORY INTEGRAL ESTIMATES AWAY FROM THE ENDPOINT
SHARP BOUNDS FOR MULTILINEAR CURVED KAKEYA, RESTRICTION AND OSCILLATORY INTEGRAL ESTIMATES AWAY FROM THE ENDPOINT
复制标题
多线性曲线 KAKEYA 的锐界、限制和远离端点的振荡积分估计
作者：
T. Tao
我们重新审视的多线性Kakeya，弯曲Kakeya，限制，振荡积分估计，在文件中获得的班尼特，Carbery，和作者使用热流单调性方法应用于分数笛卡尔积，连同归纳尺度参数。这些估计中的许多都包含了对于某个比例因子R$的形式为R^\vareps $（或$\log^{O（1）} R$）的损失。通过进一步发展热流方法，并首次将其直接应用于多线性曲线Kakeya和限制设置，我们能够消除这些损失，只要指数$p$远离端点。特别地，我们建立了远离端点的全局多线性约束估计，在超曲面上没有任何曲率假设。
We revisit the multilinear Kakeya, curved Kakeya, restriction, and oscillatory integral estimates that were obtained in paper of Bennett, Carbery, and the author using a heat flow monotonicity method applied to a fractional Cartesian product, together with induction on scales arguments. Many of these estimates contained losses of the form $R^\varepsilon$ (or $\log^{O(1)} R$) for some scale factor $R$. By further developing the heat flow method, and applying it directly for the first time to the multilinear curved Kakeya and restriction settings, we are able to eliminate these losses, as long as the exponent $p$ stays away from the endpoint. In particular, we establish global multilinear restriction estimates away from the endpoint, without any curvature hypotheses on the hypersurfaces.
影响因子：
4.9
作者：
Bourgain, Jean;Demeter, Ciprian
通讯作者：
Demeter, Ciprian