Subharmonicity of higher dimensional exponential transforms

Details Subharmonicity of higher dimensional exponential transforms Subharmonicity of higher dimensional exponential transforms

2009-02-16

arxiv.org/abs/0902.2742v1

Oper. Theory Adv. Appl., V.156, Birkhauser, 2005, 257--277

Mathematics

Functional Analysis

21 pages

Scientific paper

10.1007/3-7643-7316-4_13

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 $R^n$ ($\alpha=n$) of a density $0\leq \rho\leq 1$ 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).

Affiliated with

Also associated with

No associations

Rating

Subharmonicity of higher dimensional exponential transforms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Subharmonicity of higher dimensional exponential transforms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Subharmonicity of higher dimensional exponential transforms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-463591