An inequality type condition for quasinearly subharmonic functions and applications
Analysis of PDEs
2017-01-17 v1
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.
Cite
@article{arxiv.1509.05829,
title = {An inequality type condition for quasinearly subharmonic functions and applications},
author = {Juhani Riihentaus},
journal= {arXiv preprint arXiv:1509.05829},
year = {2017}
}
Comments
17 pages, a talk in the conference Positivity VII, Leiden 22-26 July 2013, Zaanen Centennial Conference, in: Trends in Mathematical Series, Birkh\"auser, to appear