Invariant Subspaces for Classical Operators on Weighted Spaces of Holomorphic Functions

被引：0
作者：
Alexander V. Abanin
Pham Trong Tien
机构：
[1] Southern Federal University,
[2] Southern Mathematical Institute,undefined
[3] Hanoi University of Science,undefined
[4] VNU,undefined
来源：
Integral Equations and Operator Theory | 2017年 / 89卷
关键词：
Weighted spaces of holomorphic functions; Integration operator; Differentiation operator; Invariant subspaces; Bergman spaces; Bloch spaces; Dirichlet spaces; Fock spaces; Primary 47B38; 47A15; Secondary 46E15;
D O I：
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中图分类号：
学科分类号：
摘要：
We develop an approach to describe invariant subspaces of the integration operator on various scales of weighted spaces of holomorphic functions on the unit disk and the complex plane. It allows us to solve the problem for wide classes of Bergman, Bloch, Dirichlet, and Fock spaces, while all previous known results concern spaces defined by some weights of a special form. In addition, we also show that an analogous method works as well for the differentiation operator on weighted spaces of entire functions.
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页码：409 / 438
页数：29
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