非对称区间上调和函数的Schwarz引理

Schwarz Lemma for Harmonic Functions in Asymmetric Interval

研究单位球到给定一般区间上的实调和函数的Schwarz型引理.运用调和函数的平均值定理,将像域在对称区间[-1,1]上的调和函数的Schwarz引理推广到在一般区间[a,b]上.作为一个应用,改进了Partyka和Sakan的一个结果,得到实调和函数的下界估计.

In this paper,we investigate the Schwarz lemma for real harmonic functions of the unit ball into a general interval.By appealing to the method of mean-value theorem of harmonic functions,we obtain the Schwarz lemma of harmonic functions with their image domains generalized from the symmetric interval[-1,1]to a general interval[a,b].As an application of this result,we improve the upper bound estimate given by Partyka and Sakan.Moreover,a lower bound for this class of harmonic functions is also given.