论文标题
改进的光谱投影估计值
Improved spectral projection estimates
论文作者
论文摘要
我们在非阳性曲率的歧管上获得了新的改进的光谱投影估计，其中包括用于一般托里的相对较大光谱窗口的锋利。我们的结果比第一和第三作者的早期作品[6]中的结果要强，并且论点已经大大简化了。我们更直接地利用了Berard [2]工作中隐含的重点估计值，并避免使用以前的作品中使用的弱型空间[6]和[22]。我们还通过利用微局部$ l^2 \到l^{q_c} $ kakeya-nikodym估计并避免使用$ l^2 \ of l^2 $ to l^2 $的人来简化和加强双线性参数。这使我们能够证明负曲率流形和一些新的尖锐估计值的新结果。我们在两个维度上还拥有新的和改进的技术，用于非阳性曲率的一般流形。
We obtain new improved spectral projection estimates on manifolds of non-positive curvature, including sharp ones for relatively large spectral windows for general tori. Our results are stronger than those in an earlier work of the first and third authors [6], and the arguments have been greatly simplified. We more directly make use of pointwise estimates that are implicit in the work of Berard [2] and avoid the use of weak-type spaces that were used in the previous works [6] and [22]. We also simplify and strengthen the bilinear arguments by exploiting the use of microlocal $L^2\to L^{q_c}$ Kakeya-Nikodym estimates and avoiding the of $L^2\to L^2$ ones as in earlier results. This allows us to prove new results for manifolds of negative curvature and some new sharp estimates for tori. We also have new and improved techniques in two dimensions for general manifolds of non-positive curvature.
