论文标题
$ \ mathbb {c}^3 $中复杂多项式曲线的统一卷积和傅立叶限制估计值
Uniform Convolution and Fourier Restriction estimates for complex polynomial curves in $\mathbb{C}^3$
论文作者
论文摘要
我们为两种与三维复杂多项式曲线相关的估计值建立了最佳$（p，q）$范围。这些是对傅立叶变换为复杂多项式曲线的加权限制的估计值，以及与复杂多项式曲线相关的加权卷积算子。建立这些估计值归结为建立了与相关复杂曲线相关的映射的雅各布的下限。
We establish optimal $(p,q)$ ranges for two types of estimates associated to three dimensional complex polynomial curves. These are the estimates for the weighted restriction of the Fourier Transform to a complex polynomial curve, and the weighted Convolution Operator associated to a complex polynomial curve. Establishing these estimates comes down to establishing a lower bound for the Jacobian of a mapping associated to the complex curve in question.
