Some inequalities for self-mappings of unit ball satisfying the invariant Laplacians
引用次数: 1
Abstract
In this paper, we study those mappings in unit ball satisfying the Dirichlet problem of the following differential operators
$$\begin{aligned} \Delta _{\gamma }=\big (1-|x|^{2}\big )\cdot \left[ \frac{1-|x|^{2}}{4}\cdot \sum _{i}\frac{\partial ^{2}}{\partial x_{i}^{2}}+\gamma \sum _{i}x_{i}\cdot \frac{\partial }{\partial x_{i}}+\gamma \left( \frac{n}{2}-1-\gamma \right) \right] . \end{aligned}$$Our aim is to establish the Schwarz type inequality, Heinz-Schwarz type inequality and boundary Schwarz inequality for those mappings.
满足不变拉普拉斯算子的单位球自映射的若干不等式
本文研究了单位球上满足以下微分算子Dirichlet问题的映射$$\begin{aligned} \Delta _{\gamma }=\big (1-|x|^{2}\big )\cdot \left[ \frac{1-|x|^{2}}{4}\cdot \sum _{i}\frac{\partial ^{2}}{\partial x_{i}^{2}}+\gamma \sum _{i}x_{i}\cdot \frac{\partial }{\partial x_{i}}+\gamma \left( \frac{n}{2}-1-\gamma \right) \right] . \end{aligned}$$，目的是建立这些映射的Schwarz型不等式、Heinz-Schwarz型不等式和边界Schwarz不等式。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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