论文标题
傅里叶积分运算符的方形功能估算和本地平滑
Square function estimates and Local smoothing for Fourier Integral Operators
论文作者
论文摘要
我们证明了guth-wang-zhang的平方函数估计值的可变系数版本。通过概念概念的经典论点 - 索格（Sogge），这意味着满足电影曲率条件的$ 2+1 $尺寸傅立叶积分算子的全部尖锐局部平滑估计值。特别是，紧凑的riemannian表面上的波动方程的局部平滑猜想已经完全解决。
We prove a variable coefficient version of the square function estimate of Guth--Wang--Zhang. By a classical argument of Mockenhaupt--Seeger--Sogge, it implies the full range of sharp local smoothing estimates for $2+1$ dimensional Fourier integral operators satisfying the cinematic curvature condition. In particular, the local smoothing conjecture for wave equations on compact Riemannian surfaces is completely settled.
