复线性微分方程在Orlicz型空间上解的性质
Properties of Solutions of Complex Linear Differential Equations in Orilicz Type Spaces
DOI: 10.12677/PM.2021.112038, PDF,    国家自然科学基金支持
作者: 黄星星, 杨丛丽*, 罗 颜：贵州师范大学数学科学学院，贵州 贵阳
关键词: Bloch-Orilicz空间；级；解析函数；Bloch-Orilicz Spaces； Order； Analytic Functions
摘要: 复线性微分方程，f(k)+Ak-1(Z)f(k-1)+…+A0(Z)f=F(Z)在不同空间上解的性质被许多学者研究，如Hardy空间，Dirichket空间等等，在这些空间上考虑了解的函数空间属性。在该文章中，我们主要研究了该方程在γ-Bloch-Orilicz空间上解的函数空间属性以及解的增长性，其中Aj(Z)(j=0,1,…,k-1),F(Z)是单位D={|z|<1}上的解析函数。
Abstract: The properties of the solution of the following complex linear differential equation f(k)+AK-1(Z)f(k-1)+…+A0(Z)f=F(Z) is studied in some spaces as the weighted Hardy spaces and Dirichlet spaces, the properties of the solutions of the complex linear differential equations in these spaces is considered. In this paper, some results of the properties and growth of solutions of the equations are obtained in γ-Bloch-Orilicz spaces, where Aj(Z)(j=0,1,…,k-1),F(Z) are analytic in the unit disc D={|z|<1}.
文章引用：黄星星, 杨丛丽, 罗颜. 复线性微分方程在Orlicz型空间上解的性质[J]. 理论数学, 2021, 11(2): 282-290. https://doi.org/10.12677/PM.2021.112038

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