Hardy空间单连通域上的Carleson测度  

Carleson Measure on Simply Connected Domains for Hardy Space

作　　者：王贤兴 刘梅 

机构地区：[1]贵州师范大学数学科学学院,贵州 贵阳

出　　处：《理论数学》2024年第4期45-52,共8页Pure Mathematics

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。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.

关 键 词：CARLESON测度 HARDY空间 小Carleson测度 

分 类 号：O17[理学—数学]