指数Orlicz空间中离散函数的估计
Estimates of the Discrepancy Function in Exponential Orlicz Spaces
摘要：
本文证明了在n ≥ 3的所有维数上，对于任意整数N，存在基数点分布$ N$，其相关的偏差函数D_N满足指数Orlicz类exp）L^{2/（n+1）}中N的急剧增长率的估计.这一点最近已被M.~证明。Skriganov，使用二进制数字网的随机数字移位，建立在W.L.~ Chen和M.~斯克里加诺夫我们独立开发的方法是对Skriganov方法的补充。
英文摘要：
We prove that in all dimensions n at least 3, for every integer N there exists a distribution of points of cardinality $ N$, for which the associated discrepancy function D_N satisfies the estimate an estimate, of sharp growth rate in N, in the exponential Orlicz class exp)L^{2/(n+1)}. This has recently been proved by M.~Skriganov, using random digit shifts of binary digital nets, building upon the remarkable examples of W.L.~Chen and M.~Skriganov. Our approach, developed independently, complements that of Skriganov.
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