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Invariant Subspaces for Classical Operators on Weighted Spaces of Holomorphic Functions

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Abstract

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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Authors and Affiliations

  1. Southern Federal University, Rostov-on-Don, Russian Federation, 344090

    Alexander V. Abanin

  2. Southern Mathematical Institute, Vladikavkaz, Russian Federation, 362027

    Alexander V. Abanin

  3. Hanoi University of Science, VNU, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Pham Trong Tien

Authors
  1. Alexander V. Abanin
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  2. Pham Trong Tien
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Correspondence to Alexander V. Abanin.

Additional information

The research of A.V. Abanin was supported by Russian Foundation for Basic Research under Project 15-01-01404 a.

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Abanin, A.V., Tien, P.T. Invariant Subspaces for Classical Operators on Weighted Spaces of Holomorphic Functions. Integr. Equ. Oper. Theory 89, 409–438 (2017). https://doi.org/10.1007/s00020-017-2401-y

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  • DOI: https://doi.org/10.1007/s00020-017-2401-y

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