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调和函数的Lipschitz型空间和Landau-Bloch型定理
陈少林, Miodrag MATELJEVIĆ, Saminathan PONNUSAMY, 王仙桃
数学学报 ›› 2017, Vol. 60 ›› Issue (6) : 1025-1036.
PDF(497 KB)
PDF(497 KB)
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
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 Bn of Rn, 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.
Schwarz-Pick型引理 / 调和函数 / Lipschitz型空间 / Poisson方程 {{custom_keyword}} /
Schwarz-Pick type lemma / harmonic function / Lipschitz type space / Poisson equation {{custom_keyword}} /
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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）
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