论文标题
离散球形最大函数的无维度估计值
Dimension-free estimates for the discrete spherical maximal functions
论文作者
论文摘要
We prove that the discrete spherical maximal functions (in the spirit of Magyar, Stein and Wainger) corresponding to the Euclidean spheres in $\mathbb Z^d$ with dyadic radii have $\ell^p(\mathbb Z^d)$ bounds for all $p\in[2, \infty]$ independent of the dimensions $d\ge 5$.我们论点的一个重要部分是在没有尺寸的乘法误差项的平方的警告问题中的渐近公式。通过考虑新的近似乘数，我们将展示如何吸收尺寸的指数（例如$ c^d $，对于某些$ c> 1 $），这是由于Magyar，Stein和Wainger的采样原理引起的，并最终推断出离散的球形最大功能的尺寸估计。
We prove that the discrete spherical maximal functions (in the spirit of Magyar, Stein and Wainger) corresponding to the Euclidean spheres in $\mathbb Z^d$ with dyadic radii have $\ell^p(\mathbb Z^d)$ bounds for all $p\in[2, \infty]$ independent of the dimensions $d\ge 5$. An important part of our argument is the asymptotic formula in the Waring problem for the squares with a dimension-free multiplicative error term. By considering new approximating multipliers we will show how to absorb an exponential in dimension (like $C^d$ for some $C>1$) growth in norms arising from the sampling principle of Magyar, Stein and Wainger, and ultimately deduce dimension-free estimates for the discrete spherical maximal functions.
