Composition operators on the Dirichlet space of the upper half-plane

被引：0

作者：

Sharma, Ajay K. ^{[1
]}

Sharma, Mehak ^{[1
]}

Raj, Kuldip ^{[2
]}

机构：

[1] Cent Univ Jammu, Dept Math, Samba 181143, J&K, India

[2] Shri Mata Vaishno Devi Univ, Dept Math, Katra 18232, J&K, India

来源：

NEW YORK JOURNAL OF MATHEMATICS | 2019年 / 25卷

关键词：

composition operator; upper-half plane; Hardy space; Bergman space; Dirichlet space; counting function; HARDY-SPACES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known that Hardy and weighted Bergman spaces of the upper half-plane do not support compact composition operators (see [M99] and [SS03]). In this paper, we prove that unlike Hardy and Bergman spaces, the Dirichlet space of the upper half-plane does support compact composition operators. Furthermore, bounded analytic symbols, which in the case of Hardy and weighted Bergman spaces of the upper half-plane do not even induce bounded composition operators, can induce compact composition operators on the Dirichlet space of the upper half-plane.

引用

页码：198 / 206

页数：9

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