论文标题
一些尖锐的schwarz-pick型估计及其对谐波和pluriharmonic功能的应用
Some sharp Schwarz-Pick type estimates and their applications of harmonic and pluriharmonic functions
论文作者
论文摘要
本文的目的是研究谐波或多脑功能的Schwarz-Pick型不平等。通过类似于广义的哈文森的猜想，我们首先给出了一些对欧几里得单位球的谐波功能规范的尖锐估计，以$ \ mathbb {r}^n $中的单位球，以$ \ mathbb {r}^n $。接下来，我们从$ \ mathbb {c}^n $中给出了几种尖锐的Schwarz-pick型不等式，以用于欧几里得单位球或从$ \ mathbb {c}^n $中的单位polydisc中的euclidean单位球，以进入Minkowski Space的单位球。此外，我们为Minkowski空间中定义的Pluriharmonic功能建立了一些尖锐的系数Schwarz-pick不平等现象。最后，我们使用获得的Schwarz-pick型不平等，讨论Lipschitz的连续性，任意顺序的Schwarz-Pick型引理以及谐波或Pluriharmonic函数的Bohr现象。
The purpose of this paper is to study the Schwarz-Pick type inequalities for harmonic or pluriharmonic functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimates of the norm of harmonic functions from the Euclidean unit ball in $\mathbb{R}^n$ into the unit ball of the real Minkowski space. Next, we give several sharp Schwarz-Pick type inequalities for pluriharmonic functions from the Euclidean unit ball in $\mathbb{C}^n$ or from the unit polydisc in $\mathbb{C}^n$ into the unit ball of the Minkowski space. Furthermore, we establish some sharp coefficient type Schwarz-Pick inequalities for pluriharmonic functions defined in the Minkowski space. Finally, we use the obtained Schwarz-Pick type inequalities to discuss the Lipschitz continuity, the Schwarz-Pick type lemmas of arbitrary order and the Bohr phenomenon of harmonic or pluriharmonic functions.
