Abstract
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
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