低维超平面附近集合的Phragmén-Lindelöf定理和p-调和测度
Phragmén-Lindelöf theorems and p-harmonic measures for sets near low-dimensional hyperplanes
摘要：
本文证明了$p$ -调和测度$p \in (n-m, \infty]$的估计，对于$\mathbf{R}^n$中接近于$m$ -维超平面$Λ\subset \mathbf{R}^n$，$m \in [0,n-1]$的集合.利用这些估计，我们得到了无界区域$Ω\subset \mathbf{R}^n\setminus Λ$中关于$p$ -下调和函数的Phragmén-Lindelöf型结果.此外，我们给出了局部和整体增长估计$p$ -调和函数，消失的集合在$\mathbf{R}^n$，这是接近$m$维超平面。
英文摘要：
We prove estimates of a $p$-harmonic measure, $p \in (n-m, \infty]$, for sets in $\mathbf{R}^n$ which are close to an $m$-dimensional hyperplane $Λ\subset \mathbf{R}^n$, $m \in [0,n-1]$. Using these estimates, we derive results of Phragmén-Lindelöf type in unbounded domains $Ω\subset \mathbf{R}^n\setminus Λ$ for $p$-subharmonic functions. Moreover, we give local and global growth estimates for $p$-harmonic functions, vanishing on sets in $\mathbf{R}^n$, which are close to an $m$-dimensional hyperplane.
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