论文标题
在重排三角系统的Weyl乘数上
On Weyl multipliers of the rearranged trigonometric system
论文作者
论文摘要
我们证明条件\ begin {equination} \ sum_ {n = 1}^\ infty \ frac {1} {nw（n）} <\ infty \ end \ end {equination}对于越来越多的$ w（n）$越来越多的序列是无处不在的weverentialal covergence weyl weyl Multiplormet的序列。 Haar，Walsh，Franklin和其他一些古典正交系统的属性很久以前。该结果的证明是基于与重新排列的三角系统相关的主要操作员的$ l^2 $上的新的尖锐对数下限。
We prove that the condition \begin{equation} \sum_{n=1}^\infty\frac{1}{nw(n)}<\infty \end{equation} is necessary for an increasing sequence of numbers $w(n)$ to be an almost everywhere unconditional convergence Weyl multiplier for the trigonometric system. This property for Haar, Walsh, Franklin and some other classical orthogonal systems was known long ago. The proof of this result is based on a new sharp logarithmic lower bound on $L^2$ of the majorant operator related to the rearranged trigonometric system.
