Open Access

Quasi-Nearly Subharmonicity and Separately Quasi-Nearly Subharmonic Functions

Journal of Inequalities and Applications20082008:149712

https://doi.org/10.1155/2008/149712

Received: 29 February 2008

Accepted: 30 July 2008

Published: 3 August 2008

Abstract

Wiegerinck has shown that a separately subharmonic function need not be subharmonic. Improving previous results of Lelong, Avanissian, Arsove, and of us, Armitage and Gardiner gave an almost sharp integrability condition which ensures a separately subharmonic function to be subharmonic. Completing now our recent counterparts to the cited results of Lelong, Avanissian and Arsove for so-called quasi-nearly subharmonic functions, we present a counterpart to the cited result of Armitage and Gardiner for separately quasinearly subharmonic function. This counterpart enables us to slightly improve Armitage's and Gardiner's original result, too. The method we use is a rather straightforward and technical, but still by no means easy, modification of Armitage's and Gardiner's argument combined with an old argument of Domar.

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Authors’ Affiliations

(1)
Department of Physics and Mathematics, University of Joensuu

Copyright

© Juhani Riihentaus. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.