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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