Subharmonicity of higher dimensional exponential transforms
| dc.creator | Tkachev, Vladimir | |
| dc.date | 2009-02-16 | |
| dc.date.accessioned | 2026-07-07T12:42:18Z | |
| dc.date.available | 2026-07-07T12:42:18Z | |
| dc.description | Our main result is an extension of the classical Cauchy inequality for the case of bounded densities. In particular, this implies subharmonicity of the function $M_n(E)$, where $V_n(x)$ is the critical Riesz potential in $R^n$ ($α=n$) of a density $0\leq ρ\leq 1$ and $M_n(t)$ is the profile function: the solution of $y'(t)=1-y^{n/2}(t)$, $y(0)=0$. We show thath this result is optimal (in the sense that $M_n(E)$ is harmnoic for characteristic functions of a ball) and give thereby an affirmative answer to one question posed by B. Gustafsson and M. Putinar (Ind. Univ. Math. J., 52(2003), 527-568). | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/0902.2742 | |
| dc.identifier | http://arxiv.org/abs/0902.2742 | |
| dc.identifier | Oper. Theory Adv. Appl., V.156, Birkhauser, 2005, 257--277 | |
| dc.identifier | doi:10.1007/3-7643-7316-4_13 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220031 | |
| dc.subject | Functional Analysis | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 31C05; 31B15; 44A12 | |
| dc.title | Subharmonicity of higher dimensional exponential transforms | |
| dc.type | text |