On the Closures of Dirichlet Type Spaces in the Bloch Space

被引：18

作者：

Bao, Guanlong ^{[1
]}

Gogus, Nihat Gokhan ^{[2
]}

机构：

[1] Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China

[2] Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkey

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2019年 / 13卷 / 01期

基金：

中国博士后科学基金;

关键词：

The Bloch space; Dirichlet type spaces; Closure; Interpolating Blaschke product; CARLESON MEASURES; ANALYTIC-FUNCTIONS; MULTIPLIERS; OPERATORS; FAMILY;

D O I：

10.1007/s11785-017-0676-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, via high order derivatives and via embedding derivatives of Bloch type functions into Lebesgue spaces, we characterize the closures of Dirichlet type spaces in the Bloch space. We obtain the inclusion relation between the closures and the little Bloch space. We consider the separability of the closures as Banach spaces. A criterion for an interpolating Blaschke product to be in the closures is given. We also consider the relation between the closures and the space of bounded analytic functions.

引用

页码：45 / 59

页数：15

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