论文标题
外部功能和统一的集成性
Outer functions and uniform integrability
论文作者
论文摘要
我们表明，如果$ f $是外部功能，而在[0,1）$中的$ a \，则表明$ \ {\ log |（f \ circin）^*|：ψ：\ Mathcal {d} \ to \ Mathcal {D} \ Mathcal {D} \ text} \ text {holomorphic} is Ontry On On On an une a Ontry On Aution coption。作为一个应用程序，我们得出了一个简单的证明，即如果$ f $是外部的，并且$ ϕ：\ MATHCAL {d} \ to \ MATHCAL {d} $是holomorphic，则$ f \ circcadcad $是外部。
We show that, if $f$ is an outer function and $a\in[0,1)$, then the set of functions $\{\log |(f\circψ)^*|: ψ:\mathcal{D}\to\mathcal{D} \text{ holomorphic}, |ψ(0)|\le a\}$ is uniformly integrable on the unit circle. As an application, we derive a simple proof of the fact that, if $f$ is outer and $ϕ:\mathcal{D}\to\mathcal{D}$ is holomorphic, then $f\circϕ$ is outer.
