2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61626We give a characterization of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. This includes the converse of an inequality of Beardon's for subharmonic functions. We also obtain integral inequalities of Harnack type between these two means in general domains.9 pagesAnalysis of PDEsClassical Analysis and ODEs31B05text