An inequality type condition for quasinearly subharmonic functions and applications

Abstract

Generalizing older works of Domar and Armitage and Gardiner, we give an inequality for quasinearly subharmonic functions. As an application of this inequality, we improve Domar's, Rippon's and our previous results concerning the existence of the largest subharmonic minorant of a given function. Moreover, and as an another application, we give a sufficient condition for a separately quasinearly subharmonic function to be quasinearly subharmonic. Our result contains the previous results of Lelong, of Avanissian, of Arsove, of Armitage and Gardiner, and of ours.

17 pages, a talk in the conference Positivity VII, Leiden 22-26 July 2013, Zaanen Centennial Conference, in: Trends in Mathematical Series, Birkhäuser, to appear

References in corpus (2)

• Subharmonic functions, generalizations and separately subharmonic functions
• Quasi-nearly subharmonicity and separately quasi-nearly subharmonic functions

Cited by in corpus (1)

• Removability results for subharmonic functions, for separately subharmonic functions, for harmonic functions, for separately harmonic functions and for holomorphic functions, a survey