Mathematics – Analysis of PDEs
Scientific paper
2008-02-25
Journal of Inequalities and Applications, Volume 2008 (2008), Article ID 149712, 15 pages
Mathematics
Analysis of PDEs
Some misprints of the previous version arXiv:0802.3505v1, 25 Feb 2008, corrected, some final publication details and also a co
Scientific paper
10.1155/2008/149712
Wiegerinck has shown that a separately subharmonic function need not be subharmonic. Improving previous results of Lelong, of Avanissian, of 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 quasi-nearly subharmonic functions. 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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