论文标题
关于与张 - 惠森 - 沃尔夫定理相关的钟声功能：案例研究
On a Bellman function associated with the Chang--Wilson--Wolff theorem: a case study
论文作者
论文摘要
在本文中，我们估算了分布的尾巴（即，对于那些功能$ f $，其二元平方函数由给定常数界定的那些函数$ f $。特别是，我们的估计值比Chang-Willson-狼定理的估计值要好一些。在论文中，我们调查了与问题相对应的钟声功能。发现了此功能的一个奇怪结构：它具有第一个衍生物的跳跃，以$ [0,1] $的密集子集（准确地计算出它），但它为$ c^\ infty $ -Class，对于$ x>> \ sqrt3 $（在此计算到乘数常数的位置））。 本文的一个不寻常的特征在于证明中计算机计算的使用。然而，所有证明都非常严格，因为只有整数算术被分配给计算机。
In this paper we estimate the tail of distribution (i.e., the measure of the set $\{f\ge x\}$) for those functions $f$ whose dyadic square function is bounded by a given constant. In particular we get a bit better estimate than the estimate following from the Chang--Wilson--Wolf theorem. In the paper we investigate the Bellman function corresponding to the problem. A curious structure of this function is found: it has jumps of the first derivative at a dense subset of interval $[0,1]$ (where it is calculated exactly), but it is of $C^\infty$-class for $x>\sqrt3$ (where it is calculated up to a multiplicative constant). An unusual feature of the paper consists in the usage of computer calculations in the proof. Nevertheless, all the proofs are quite rigorous, since only the integer arithmetic was assigned to computer.
