论文标题
核苷的端线双线性限制估计值
An endline bilinear restriction estimate for paraboloids
论文作者
论文摘要
我们证明了$ l^2 \ times l^2 \ to l^q_tl^r_x $ biinear expoint fourier限制估计估计$ n $ - 二维椭圆抛物面，带有$ n \ ge 2 $和$ 1 \ le q \ le q \ le q \ le \ le \ le \ iffty $，$ 1 \ le r \ le r \ le r \ le \ le \ le \ le \ le \ le \ le \ le \ le 2 $ $ \ frac {1} {q} = \ frac {n+1} {2} \ bigl（1- \ frac {1} {r} {r} \ bigr）$，除关键索引外。这包括当$ q = r = \ frac {n+3} {n+1} $时的端点情况，这是一个在tao \ cite {taogfa}中留下的问题。除关键指数外，它还提高了Lee-Vargas \ cite {leevargas}的尖锐的非端线结果，以确认椭圆形抛物面的Foschi和Klainerman \ cite {fokl}精神的猜想。我们的证明是通过将基于波浪柜理论的\ emph {深刻}归纳策略结合在一起来实现的，而下降方法都来自\ cite {taomz}。
We prove an $L^2\times L^2\to L^q_tL^r_x$ bilinear adjoint Fourier restriction estimate for $n$-dimensional elliptic paraboloids, with $n\ge 2$ and $1\le q \le \infty$, $1\le r\le 2$ being on the endline $\frac{1}{q}=\frac{n+1}{2}\bigl(1-\frac{1}{r}\bigr)$ except for the critical index. This includes the endpoint case when $q=r=\frac{n+3}{n+1}$, a question left unsettled in Tao \cite{TaoGFA}. Apart from the critical index, it improves the sharp non-endline result of Lee-Vargas \cite{LeeVargas} to the full range, confirming a conjecture in the spirit of Foschi and Klainerman \cite{FoKl} on the elliptic paraboloid. Our proof is accomplished by uniting the \emph{profound} induction-on-scale tactics based on the wave-table theory and the method of descent both stemming from \cite{TaoMZ}.
