AI 中文总结
本文通过几何量估计解析函数空间上求值泛函的范数，刻画了支撑具有有界导数的无界解析函数的单连通域，部分解决了海曼列表中的问题1.45。
AI 中文摘要
本文给出了复平面中支撑具有有界导数的无界解析函数的单连通域的几何刻画，为海曼列表中的问题1.45提供了部分解答。对于给定的单连通域，该刻画通过在该域上的一个合适的解析函数巴拿赫空间上，用几何量对某些求值泛函的范数进行上下估计来实现。
英文摘要
In this paper we provide a geometric characterization of simply connected domains in the complex plane supporting an unbounded analytic function with bounded derivative, providing a partial answer to Problem 1.45 in the Hayman List. For a given simply connected domain this characterization is achieved by estimating above and below the norms of certain evaluation functionals on a suitable Banach space of analytic functions on that domain by geometric quantities.
Comments15 Pages, 4 Figures
