An inequality type condition for quasinearly subharmonic functions and applications

摘要

Generalizing older works of Domar and Armitage and Gardiner, we give aninequality for quasinearly subharmonic functions. As an application of thisinequality, we improve Domar's, Rippon's and our previous results concerningthe existence of the largest subharmonic minorant of a given function.Moreover, and as an another application, we give a sufficient condition for aseparately quasinearly subharmonic function to be quasinearly subharmonic. Ourresult contains the previous results of Lelong, of Avanissian, of Arsove, ofArmitage and Gardiner, and of ours.