COMPACT COMPOSITION OPERATORS ON HARDY-ORLICZ SPACES

被引：0

作者：

Sharma, Ajay K. ^{[1
]}

Sharma, S. D. ^{[1
]}

机构：

[1] Univ Jammu, Dept Math, Jammu 180006, India

来源：

MATEMATICKI VESNIK | 2008年 / 60卷 / 03期

关键词：

Hardy-Orlicz space; Composition operator; Nevanlinna counting function; vanishing Carleson measure;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, compact composition operators acting on Hardy-Orlicz spaces H-Phi = {f is an element of H(D) : (sup)(0<r<1) integral(partial derivative D) Phi(log(+) vertical bar f(re(i theta))vertical bar) d sigma < infinity} are studied. In fact, we prove that if Phi is a twice differentiable, non-constant, non-decreasing non-negative, convex function on R, then the composition operator C-phi induced by a holomorphic self-map phi of the unit disk is compact on Hardy-Orlicz spaces H-Phi if and only if it is compact on the Hardy space H-2.

引用

页码：215 / 224

页数：10

共 14 条

[1] Compact composition operators on the Nevanlinna class [J].