doi:10.1016/j.jmaa.2020.124131engGalé, José E.Matache, ValentinMiana, Pedro J.Sánchez-Lajusticia, LuisHilbertian Hardy-Sobolev spaces on a half-planeART-2020-117712In this paper we deal with a scale of reproducing kernel Hilbert spaces H2 (n), n=0, which are linear subspaces of the classical Hilbertian Hardy space on the right-hand half-plane C+. They are obtained as ranges of the Laplace transform in extended versions of the Paley-Wiener theorem which involve absolutely continuous functions of higher degree. An explicit integral formula is given for the reproducing kernel Kz, n of H2 (n), from which we can find the estimate ¿Kz, n¿~|z|-1/2 for z¿C+. Then composition operators Cf:H2 (n)¿H2 (n), Cff=f°f, on these spaces are discussed, giving some necessary and some sufficient conditions for analytic maps f:C+¿C+ to induce bounded composition operators.2020http://zaguan.unizar.es/record/13078910.1016/j.jmaa.2020.124131http://zaguan.unizar.es/record/130789oai:zaguan.unizar.es:130789info:eu-repo/grantAgreement/ES/DGA/E26-17Rinfo:eu-repo/grantAgreement/ES/MCYTS-MTM2016-77710-PJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 489, 1 (2020), 124131 1-25by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess