Domination conditions for families of quasinearly subharmonic functions
  Domar has given a condition that ensures the existence of the largest subharmonic minorant of a given function. Later Rippon pointed out that a modification of Domar's argument gives in fact a better result. Using our previous, rather general and flexible, modification of Domar's original argument, we extend their results both to the subharmonic and quasinearly subharmonic settings. 
Juhani Riihentaus
math.CA