COMPACT COMPOSITION OPERATORS ON THE BLOCH SPACE

被引：487

作者：

MADIGAN, K ^{[1
]}

MATHESON, A ^{[1
]}

机构：

[1] LAMAR UNIV,DEPT MATH,BEAUMONT,TX 77710

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1995年 / 347卷 / 07期

关键词：

COMPOSITION OPERATOR; COMPACT OPERATOR; BLOCH SPACE; CUSP;

D O I：

10.2307/2154848

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Necessary and sufficient conditions are given for a composition operator C(phi)f = o phi to be compact on the Bloch space B and on the little Bloch space B-0. Weakly compact composition operators on B-0 are shown to be compact. If phi is an element of B-0 is a conformal mapping of the unit disk D into itself whose image phi(D) approaches the unit circle T only in a finite number of nontangential cusps, then C-phi is compact on B-0 On the other hand if there is a point of T boolean AND phi(D) at which phi(D) does not have a cusp, then C-phi is not compact.

引用

页码：2679 / 2687

页数：9