高维指数变换的亚谐性
Subharmonicity of higher dimensional exponential transforms
摘要：
我们的主要结果是经典的柯西不等式在有界密度情形下的推广。特别是，这意味着次谐波的功能$M_n(E)$，其中$V_n(x)$是临界Riesz潜力在$R^n$（$α=n$）的密度$0\leq ρ\leq 1$和$M_n(t)$是配置文件功能：解决方案的$y'(t)=1-y^{n/2}(t)$，$y(0)=0$。我们证明了这个结果是最优的（在$M_n(E)$对球的特征函数是调和的意义上），从而对B. Gustafsson和M. Putinar（Ind. Univ. Math. J.，52（2003），527-568）。
英文摘要：
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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
