论文标题
接近最佳$ l^p \ rightarrow l^q $估计欧几里得的估计值是$ \ mathbb {r}^3 $的原型超曲面的平均值
Near Optimal $L^p\rightarrow L^q$ Estimates for Euclidean Averages Over Prototypical Hypersurfaces in $\mathbb{R}^3$
论文作者
论文摘要
我们发现$（p，q）的精确范围为$（p，q）$，对于$ \ mathbb {r}^3 $中的一类两种可变性多项式的局部平均值是有限的弱型$（p，q）$，鉴于HyperSurfaces具有欧几里得表面测量。我们使用非振荡的几何方法来得出这些结果，以与一般相对于一般的房地产案例建立牢固联系的多项式模型类别。
We find the precise range of $(p,q)$ for which local averages along graphs of a class of two-variable polynomials in $\mathbb{R}^3$ are of restricted weak type $(p,q)$, given the hypersurfaces have Euclidean surface measure. We derive these results using non-oscillatory, geometric methods, for a model class of polynomials bearing a strong connection to the general real-analytic case.
