论文标题
一个分形傅里叶限制估算的家族，对Kakeya问题产生了影响
A family of fractal Fourier restriction estimates with implications on the Kakeya problem
论文作者
论文摘要
在最近的一篇论文中[Ann。数学。 189（2019），837--861]，Du和Zhang证明了分形的傅立叶限制估算，并用它来建立Schrödinger最大功能的尖锐$ l^2 $估计，以$ \ bbb r^n $，$ n \ geq 2 $。在本文中，我们表明du-zhang估计是一个分形限制估计的终点，使得家族的每个成员（除原始）表示尖锐的kakeya导致$ \ bbb r^n $与多项式沃尔夫·沃尔夫（Wolff axioms）密切相关。我们还证明，在$ \ bbb r^2 $中，我们家庭的所有估计都是正确的。
In a recent paper [Ann. of Math. 189 (2019), 837--861], Du and Zhang proved a fractal Fourier restriction estimate and used it to establish the sharp $L^2$ estimate on the Schrödinger maximal function in $\Bbb R^n$, $n \geq 2$. In this paper, we show that the Du-Zhang estimate is the endpoint of a family of fractal restriction estimates such that each member of the family (other than the original) implies a sharp Kakeya result in $\Bbb R^n$ that is closely related to the polynomial Wolff axioms. We also prove that all the estimates of our family are true in $\Bbb R^2$.
