The Schwarz lemma in Clifford analysis
The Schwarz lemma in Clifford analysis
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DOI：
10.1090/s0002-9939-2014-11854-5
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发表时间：
2014-01
期刊：
影响因子：
--
通讯作者：
Z. Zhang
中科院分区：
文献类型：
--
作者：
Z. Zhang
本文首先给出了调和函数在Clifford分析框架下的Cauchy型积分表示，并利用Clifford分析中调和函数的积分表示，给出了调和函数的Poisson积分公式.作为应用，给出了Clifford值调和函数的中值定理和最大模定理。其次，给出了Möbius变换的一些性质，并证明了单演函数与Möbius变换之间的密切关系。最后，利用调和函数的积分表示和Möbius变换的性质，建立了调和函数和单演函数的施瓦茨型引理.
In this paper, we first give the Cauchy type integral representation for harmonic functions in the Clifford analysis framework, and by using integral representations for harmonic functions in Clifford analysis, the Poisson integral formula for harmonic functions is represented. As its application, the mean value theorems and the maximum modulus theorem for Clifford-valued harmonic functions are presented. Second, some properties of Möbius transformations are given, and a close relation between the monogenic functions and Möbius transformations is shown. Finally, by using the integral representations for harmonic functions and the properties of Möbius transformations, Schwarz type lemmas for harmonic functions and monogenic functions are established.