Outer functions and uniform integrability
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
