内相关函数的路径
Paths of inner-related functions
摘要：
刻画了$H^\infty$的子集$\cni$的连通分支，其中$b$是Carleson-Newman Blaschke乘积，$h\in H^\infty$是可逆函数.我们使用这个结果表明，除了有限的Blaschke产品，没有内函数在小Bloch空间是在这些组件之一的封闭。我们的主要结果是：在积$uh$的集合中，每一个内函数都可以与$\cni$的一个元素相连，其中$u$是内函数，$h$是可逆函数.我们还研究了道格拉斯代数的背景下，这些问题。
英文摘要：
We characterize the connected components of the subset $\cni$ of $H^\infty$ formed by the products $bh$, where $b$ is Carleson-Newman Blaschke product and $h\in H^\infty$ is an invertible function. We use this result to show that, except for finite Blaschke products, no inner function in the little Bloch space is in the closure of one of these components. Our main result says that every inner function can be connected with an element of $\cni$ within the set of products $uh$, where $u$ is inner and $h$ is invertible. We also study some of these issues in the context of Douglas algebras.
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