Lizama-Yanez, CCLizama-YanezAbadias, LucianoLucianoAbadiasGale, Jose E.Jose E.Gale2025-04-232025-04-23202310.1007/s11856-022-2353-zhttps://sic.vriic.usach.cl/entities/publication/bf679237-5774-4dfa-ba84-eaf20584f6a4We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for (C, alpha)-bounded operators, alpha > 0. This extends known results for power bounded operators to the setting of Cesaro bounded operators of fractional order, thus generalizing the results substantially. In passing, we obtain a generalization of the mean ergodic theorem in our framework. Examples are given to illustrate the theory.en-UShttps://doi.org/10.1007/s11856-022-2353-z