On the 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 modifications of Domar’s original
argument, we extend their results both to the subharmonic and to the quasinearly subharmonic
settings.