Nevanlinna–Djrbashian Classes of Functions Delta-Subharmonic in the Unit Disc

A function u is delta-subharmonic in a domain G and \(\nu \) is its associated measure, if \(u=u_1-u_2\) and \(\nu =\nu _1-\nu _2\) , where \(u_{1,2}\) are subharmonic functions in G, which possess RieszRiesz associated measures \(\nu _{1,2}\) . We say that two delta-subharmonic functions \(u=u_1-u_2\) and \(v=v_1-v_2\) are equal, if \(u_1+v_2=u_2+v_1\) everywhere in G. Besides, we assume that the associated measure \(\nu \) of u is minimally decomposed in the JordanJordan decomposition sense, i.e., \(\nu =\nu _+-\nu _-\) and \((\text{supp }\nu _+)\bigcap (\text{supp }\nu _-)=\emptyset \) , where \(\nu _{\pm }\) are positive and negative variations of \(\nu \) .