论文标题
$ l^2 $仿射傅里叶限制定理用于$ \ mathbb {r}^3 $中的平滑表面
$L^2$ affine Fourier restriction theorems for smooth surfaces in $\mathbb{R}^3$
论文作者
论文摘要
我们证明，$ \ theer $ l^2 $ l^2 $ fourier限制性不平等，用于$ \ mathbb {r}^3 $配备了具有仿射表面测量或其功率的$ \ mathbb {r}^3 $。结果对于所有平滑表面都是有效的，并且边界对于由具有有限系数的多项式的多项式图所定义的所有表面都均匀。主要工具是这些表面的解耦定理。
We prove sharp $L^2$ Fourier restriction inequalities for compact, smooth surfaces in $\mathbb{R}^3$ equipped with the affine surface measure or a power thereof. The results are valid for all smooth surfaces and the bounds are uniform for all surfaces defined by the graph of polynomials of degrees up to $d$ with bounded coefficients. The primary tool is a decoupling theorem for these surfaces.
