Invariant subspaces of the integration operators on H\"ormander algebras and Korenblum type spaces

We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex plane. Applications are given to the case of Korenblum type spaces and H"ormander algebras of entire functions.