调和函数的Lipschitz型空间和Landau-Bloch型定理  

Lipschitz Type Spaces and Landau-Bloch Type Theorems for Harmonic Functions

作　　者：陈少林 Miodrag MATELJEVIC Saminathan PONNUSAMY 王仙桃 

机构地区：[1]衡阳师范学院数学与统计学院,衡阳421008 [2]University of Belgrade,Faculty of Mathematics,Studentski Trg 16 Belgrade,11000 Serbia [3]Indian Statistical Institute,Chennai Centre,SETS,MGR Knowledge City,CIT Campus Chennai,600113 India [4]汕头大学数学系,汕头515063

出　　处：《数学学报（中文版）》2017年第6期1025-1036,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11401184,11571216);湖南省自然科学基金(2015JJ3025);湖南省青年骨干教师培养对象基金(YF1101);“运筹学与控制论”湖南省重点建设学科基金;湖南省科技计划基金(2016TP1020)

摘　　要：主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性.We investigate some properties on harmonic functions and solutions to Poisson equations. We will discuss the Lipschitz type spaces on harmonic functions. Secondly, we establish the Schwarz-Pick type lemma for harmonic functions in the unit ball B^n of R^n, and then we apply it to obtain a Landau-Bloch type theorem for harmonic functions in Hardy spaces. At last, we use a normal family argument to extend the Landau-Bloch type theorem to functions which are solutions to Poisson equations.

关 键 词：Schwarz—Pick型引理 调和函数 Lipschitz型空间 POISSON方程 

分 类 号：O177.2[理学—数学]