Subharmonic functions, generalizations and separately subharmonic functions
| dc.creator | Riihentaus, Juhani | |
| dc.date | 2006-10-08 | |
| dc.date | 2008-10-08 | |
| dc.date.accessioned | 2026-07-07T10:08:18Z | |
| dc.date.available | 2026-07-07T10:08:18Z | |
| dc.description | First, we give the definition for quasi-nearly subharmonic functions, now for general, not necessarily nonnegative functions, unlike previously. We point out that our function class incudes, among others, quasisubharmonic functions, nearly subharmonic functions (in a slightly generalized sense) and almost subharmonic functions. We also give some basic properties of quasi-nearly subharmonic functions. Second, after recalling some of the existing subharmonicity results of separately subharmonic functions, we give the corresponding counterparts for separately quasi-nearly subharmonic functions, thus improving previous results of ours, of Lelong, of Avanissian and of Arsove. Third, we give two results concerning the subharmonicity of a function subharmonic with respect to the first variable and harmonic with respect to the second variable. The first result improves a result of Arsove, concerning the case when the function has, in addition, locally a negative integrable minorant. The second result improves a result of Kołodziej and Thorbiörnson concerning the subharmonicity of a function subharmonic and ${\mathcal{C}}^2$ in the first variable and harmonic in the second. | |
| dc.description | A talk at the XIV Conference on Analytic Functions, July 22-28, 2007, Chelm, Poland. Some misprints of the previous version arXiv:math/0610259v4, 27 Dec 2007, corrected, also some final publication details added to a couple of references. In addition, the publication information is given | |
| dc.identifier | https://arxiv.org/abs/math/0610259 | |
| dc.identifier | http://arxiv.org/abs/math/0610259 | |
| dc.identifier | Scientific Bulletin of Chelm, Section of Mathematics and Computer Science, No. 2/2007, pp. 49-76. (ISBN 978-83-61149-24-8) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170947 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 31B05;31C05 | |
| dc.title | Subharmonic functions, generalizations and separately subharmonic functions | |
| dc.type | text |