Fine Boundary Behavior and Invariant Subspaces of Harmonically Weighted Dirichlet Spaces

被引：0

作者：

Dominique Guillot

机构：

[1] Pavillon Alexandre-Vachon,Département de mathématiques et de statistique

[2] Université Laval,undefined

来源：

Complex Analysis and Operator Theory | 2012年 / 6卷

关键词：

Weighted Dirichlet spaces; Dirichlet space; Radial limits; Invariant subspaces; Logarithmic capacity; Primary 46E22; Secondary 47B32;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the boundary behavior of functions in spaces of Dirichlet-type by using non-linear capacities generalizing the logarithmic capacity. We use these capacities to obtain information about the invariant subspaces of the shift operator. As an application, we prove an analogue of a conjecture of Brown and Shields when the space is weighted by the Poisson integral of a finite sum of atoms.

引用

页码：1211 / 1230

页数：19

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