Hardy空间单连通域上的Carleson测度

Carleson Measure on Simply Connected Domains for Hardy Space

摘要: Carleson测度在经典的解析函数空间之中已经有了许多漂亮的结果，那么一个很自然的问题就是：Carleson测度在一般单连通域上的解析空间中具有哪些刻画？本文继María之后，我们应用拟共形映射的相关性质将经典的Hardy空间延拓到一般单连通域上，并继续研究与在一般单连通域上定义的Hardy空间相关的Carleson测度的等价刻画。我们还研究了小Carleson测度的类比陈述。

Abstract: Carleson measures have had many beautiful results in classical analytic function spaces, so a natural question is: what are the characteristics of Carleson measures in analytic spaces on general single connected domains? Following María, we apply the correlation properties of quasi-conformal mapping to extend the classical Hardy space to the general single-connected domain, and continue to study the equivalence characterization of the Carleson measure related to the Hardy space defined on the general single-connected domain. We also looked at the analogical statements of the vanish Carleson measure.