Essential norms of composition operators and Aleksandrov measures

被引：42

作者：

Cima, JA ^{[1
]}

Matheson, AL ^{[1
]}

机构：

[1] LAMAR UNIV, BEAUMONT, TX 77710 USA

来源：

PACIFIC JOURNAL OF MATHEMATICS | 1997年 / 179卷 / 01期

关键词：

D O I：

10.2140/pjm.1997.179.59

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The essential norm of a composition operator on H-2 is calculated in terms of the Aleksandrov measures of the inducing holomorphic map. The argument provides a purely function-theoretic proof of the equivalence of Sarason's compactness condition for composition operators on L-1 and Shapiro's compactness condition for composition operators on Hardy spaces. An application is given relating the essential norm to angular derivatives.

引用

页码：59 / 64

页数：6

共 13 条

[1]

Ahlfors L. V., 1973, McGraw-Hill Series in Higher Mathematics

[2]

Aleksandrov A.B., 1987, IZV ACAD NAUK ARM SS, V22, P490

[3]

COWEN CC, 1983, J OPERAT THEOR, V9, P77

[4]

COWEN CC, 1978, J LOND MATH SOC, V26, P271