Subharmonicity of higher dimensional exponential transforms

dc.creatorTkachev, Vladimir
dc.date2009-02-16
dc.date.accessioned2026-07-07T12:42:18Z
dc.date.available2026-07-07T12:42:18Z
dc.descriptionOur 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.description21 pages
dc.identifierhttps://arxiv.org/abs/0902.2742
dc.identifierhttp://arxiv.org/abs/0902.2742
dc.identifierOper. Theory Adv. Appl., V.156, Birkhauser, 2005, 257--277
dc.identifierdoi:10.1007/3-7643-7316-4_13
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220031
dc.subjectFunctional Analysis
dc.subjectAnalysis of PDEs
dc.subject31C05; 31B15; 44A12
dc.titleSubharmonicity of higher dimensional exponential transforms
dc.typetext

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