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Quasi-nearly subharmonic functions in locally uniformly homogeneous spaces
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pavlović, Miroslav Riihentaus, Juhani |
| Copyright Year | 2011 |
| Abstract | We define nonnegative quasi-nearly subharmonic functions on so called locally uniformly homogeneous spaces. We point out that this function class is rather general. It includes quasi-nearly subharmonic (thus also subharmonic, quasisubharmonic and nearly subharmonic) functions on domains of Euclidean spaces $${{\mathbb{R}}^n}$$, n ≥ 2. In addition, quasi-nearly subharmonic functions with respect to various measures on domains of $${{\mathbb{R}}^n}$$, n ≥ 2, are included. As examples we list the cases of the hyperbolic measure on the unit ball Bn of $${{\mathbb{R}}^n}$$, the $${{\mathcal{M}}}$$-invariant measure on the unit ball B2n of $${{\mathbb{C}}^n}$$, n ≥ 1, and the quasihyperbolic measure on any domain $${D\subset {\mathbb{R}}^n}$$, $${D\ne {\mathbb{R}}^n}$$. Moreover, we show that if u is a quasi-nearly subharmonic function on a locally uniformly homogeneous space and the space satisfies a mild additional condition, then also up is quasi-nearly subharmonic for all p > 0. |
| Starting Page | 1 |
| Ending Page | 10 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s11117-009-0037-0 |
| Volume Number | 15 |
| Alternate Webpage(s) | http://poincare.matf.bg.ac.rs/~pavlovic/qns-hom.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s11117-009-0037-0 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
