调和分析中的离散模拟：球面平均
Discrete analogues in harmonic analysis: Spherical averages
摘要：
本文证明了\Bbb Z^d的离散设置中\Bbb R^d的球面极大值定理的一个类似。所使用的方法是双重的：应用某些“抽样”技术，以及在研究整数的表示数作为d平方和特别是“圆方法”时产生的想法。我们得到的结果必然限于d \ge 5，而且L^p估计的p的范围不同于\Bbb R^d中的类似估计。
英文摘要：
In this paper we prove an analogue in the discrete setting of \Bbb Z^d, of the spherical maximal theorem for \Bbb R^d. The methods used are two-fold: the application of certain "sampling" techniques, and ideas arising in the study of the number of representations of an integer as a sum of d squares in particular, the "circle method". The results we obtained are by necessity limited to d \ge 5, and moreover the range of p for the L^p estimates differs from its analogue in \Bbb R^d.
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