论文标题
近端积分运算符的局部平滑和耐寒空间
Local smoothing and Hardy spaces for Fourier integral operators on manifolds
论文作者
论文摘要
我们在带有有限的几何形状的Riemannian歧管上为傅立叶积分运算符介绍了Hardy空间。然后，我们使用这些空间来获得满足电影曲率条件的傅立叶积分运算符的改进局部平滑估计值，以及紧凑型歧管上的波动方程。估计值本质上是尖锐的，对于所有$ 2 <p <\ infty $，并且在每个紧凑型歧管上。我们还将本地平滑估计值应用于非线性波方程，并在$ l^{2} $之外的初始数据（基于sobolev空格）之外。
We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates for Fourier integral operators satisfying the cinematic curvature condition, and for wave equations on compact manifolds. The estimates are essentially sharp, for all $2<p<\infty$ and on each compact manifold. We also apply our local smoothing estimates to nonlinear wave equations with initial data outside of $L^{2}$-based Sobolev spaces.
