On a Bellman function associated with the Chang–Wilson–Wolff theorem: a case study
On a Bellman function associated with the Chang–Wilson–Wolff theorem: a case study
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与常威尔逊沃尔夫定理相关的贝尔曼函数：案例研究
DOI：
10.1090/spmj/1719
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Vasyunin, V.
中科院分区：
文献类型：
--
作者：
Nazarov, F.;Vasyunin, V.;Volberg, A.;Vasyunin, V.
对于并元平方函数受给定常数约束的那些函数，估计了分布的尾部（即集合的测度）。特别地，根据Chang-Wilson-Wolf定理的估计略有改进。研究贝尔曼函数对应的问题揭示了一个奇怪的结构，这个功能：它有跳跃的一阶导数在一个密集的子集的时间间隔（在那里它是精确计算），但它是类的（在那里它是计算到一个乘法常数）。
The tail of distribution (ie, the measure of the set) is estimated for those functionswhose dyadic square function is bounded by a given constant. In particular, an estimate following from the Chang–Wilson–Wolf theorem is slightly improved. The study of the Bellman function corresponding to the problem reveals a curious structure of this function: it has jumps of the first derivative at a dense subset of the interval(where it is calculated exactly), but it is of-class for(where it is calculated up to a multiplicative constant).