Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction
Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction
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ℝ3 中表面承载测量的傅里叶变换的统一估计及其在傅里叶限制中的应用
DOI：
10.1007/s00041-011-9191-4
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发表时间：
2010
影响因子：
1.2
通讯作者：
D. Müller
中科院分区：
文献类型：
--
作者：
I. Ikromov;D. Müller
抽象令S是${\Bbb{R}}^{3}$中的超曲面，该超曲面是光滑有限型函数φ的图，令μ=ρ
dσ是S上的面载测度，其中dσ表示S上的面元，ρ是具有足够小支撑的光滑密度。我们得到一致的估计傅立叶变换$\hat{\mu}$的μ，这是尖锐的情况下，除了主面的牛顿多面体的φ，当表示在适应的坐标，是无界的。作为应用，我们证明了在原坐标适应于φ的情况下，S的一个Lp-L2 Fourier限制定理.这改进了早期与M的联合工作。肯普
AbstractLet S be a hypersurface in ${\Bbb{R}}^{3}$ which is the graph of a smooth, finite type function φ, and let μ=ρ
dσ be a surface carried measure on S, where dσ denotes the surface element on S and ρ a smooth density with sufficiently small support. We derive uniform estimates for the Fourier transform $\hat{\mu}$ of μ, which are sharp except for the case where the principal face of the Newton polyhedron of φ, when expressed in adapted coordinates, is unbounded. As an application, we prove a sharp Lp-L2 Fourier restriction theorem for S in the case where the original coordinates are adapted to φ. This improves on earlier joint work with M. Kempe.