论文标题
通过双线性估计值对高维的倍曲底物的限制估计值
Restriction estimates for hyperboloids in higher dimensions via bilinear estimates
论文作者
论文摘要
令$ \ mathbb {h} $为$（d-1）$ - Dimensonal双曲线抛物面，$ \ Mathbb {r}^d $，让$ ef $为与$ \ Mathbb {h}相关的傅立叶扩展运算符，$ f $ f $ f $ f $ f $ b^{d-d-1}（0,0,2）$。我们证明$ \ | ef \ | _ {l^p（b（b（0，r））} \ leq c_isr^ε\ | f \ | _ {l^p} $ for $ p \ geq \ geq \ geq \ frac {2（d + 2（d + 2）}} $ \ mathbb {h} $的正主曲率和负主曲率数量之间的最小值。 S. Lee和Vargas证明了$ \ Mathbb {H} $的双线性限制估计在我们的论点中起着重要作用。
Let $\mathbb{H}$ be a $(d-1)$-dimensonal hyperbolic paraboloid in $\mathbb{R}^d$ and let $Ef$ be the Fourier extension operator associated to $\mathbb{H},$ with $f$ supported in $B^{d-1}(0,2)$. We prove that $\|Ef\|_{L^p (B(0,R))} \leq C_εR^ε\|f\|_{L^p}$ for all $p \geq \frac{2(d+2)}{d}$ whenever $ \frac{d}{2} \geq m + 1$, where $m$ is the minimum between the number of positive and negative principal curvatures of $\mathbb{H}$. Bilinear restriction estimates for $\mathbb{H}$ proved by S. Lee and Vargas play an important role in our argument.
