doi:10.1016/j.jde.2025.113465engAbadias, LucianoDe León-Contreras, MartaMahillo, AlejandroEnd-point maximal regularity for the discrete parabolic Cauchy problem and regularity of non-local operators in discrete Besov spacesART-2025-144241In this paper we prove both end-point maximal -regularity for the discrete parabolic Cauchy problem and regularity of some non-local operators in discrete Besov spaces. To that aim, we prove characterizations of the discrete Besov spaces in terms of the heat and Poisson semigroups associated with the discrete Laplacian. Moreover, we provide new estimates for the derivatives of the discrete heat kernel and semigroup which are of independent interest.2025http://zaguan.unizar.es/record/16108410.1016/j.jde.2025.113465http://zaguan.unizar.es/record/161084oai:zaguan.unizar.es:161084info:eu-repo/grantAgreement/ES/DGA/E48-23Rinfo:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00JOURNAL OF DIFFERENTIAL EQUATIONS 440 (2025), 113465 [43 pp.]by-nchttps://creativecommons.org/licenses/by-nc/4.0/deed.esinfo:eu-repo/semantics/openAccess