Some Closed Range Integral Operators on Spaces of Analytic Functions

被引：10
|
作者：
Anderson, Austin [1 ]
机构：
[1] Univ Hawaii, Dept Math, Honolulu, HI 96822 USA
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2011年 / 69卷 / 01期
基金：
美国国家科学基金会;
关键词：
Volterra operator; Cesaro operator; integral operator; bounded below; closed range; Bloch; Hardy; Bergman; BMOA; multiplication operator; WEIGHTED COMPOSITION OPERATORS; BOUNDED MEAN-OSCILLATION; BERGMAN SPACES; TOEPLITZ OPERATORS;
D O I：
10.1007/s00020-010-1827-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Our main result is a characterization of g for which the operator S(g)(f)(z) = integral(z)(0)f'(w) g(w) dw is bounded below on the Bloch space. We point out analogous results for the Hardy space H(2) and the Bergman spaces A(p) for 1 <= p < infinity. We also show the companion operator T(g)(f)(z) = integral(z)(0)f(w)g'(w) dw is never bounded below on H(2), Bloch, nor BMOA, but may be bounded below on A(p).
引用
收藏
页码：87 / 99
页数：13
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