doi:10.1007/s11856-022-2353-zengAbadias, L.Galé, J. E.Lizama, C.Poisson equation and discrete one-sided Hilbert transform for (c,a)-bounded operatorsART-2023-129846We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for (C, α)-bounded operators, α > 0. This extends known results for power bounded operators to the setting of Cesàro 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.2023http://zaguan.unizar.es/record/13080710.1007/s11856-022-2353-zhttp://zaguan.unizar.es/record/130807oai:zaguan.unizar.es:130807info:eu-repo/grantAgreement/ES/DGA/E26-17Rinfo:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00info:eu-repo/grantAgreement/ES/UZ/JIUZ-2019-CIE-01Israel Journal of Mathematics 253 (2023), 917–987All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/closedAccess