Basing our proof on an old argument of Domar, we generalize
and improve Armitage’s and Gardiner’s previous subharmonic function
inequality result. Our result is stated for quasinearly subharmonic functions, it is rather general and, at the same time, flexible. Indeed, with the
aid of it we will in the next two sections improve both Domar’s and our
previous domination condition results of subharmonic functions, and
also Armitage’s and Gardiner’s, and our results on the subharmonicity
of separately subharmonic functions.
Keywords: Subharmonic, quasinearly subharmonic, mean value,
weighted integrals, control functions
