【作者】 张颖；

【导师】 胡俊云；

【作者基本信息】 浙江师范大学 ， 基础数学， 2014， 硕士

【摘要】 本篇硕士论文集中了作者在攻读硕士期间的主要研究成果,研究了广义复合算子、微分算子与加权复合算子的乘积以及复合算子的有界性和紧性的问题.主要利用算子、范数的性质以及函数空间的定义,选取合适的检测函数,得到这些算子在解析函数空间中为有界性和紧性的几个充要条件.本文由四章组成：第一章简要叙述了加权复合算子、广义复合算子、微分算子与加权复合算子的乘积的研究背景、发展过程以及研究价值和意义,并将本文后面章节中所出现的基本概念和符号作简单的介绍.第二章讨论了单位圆盘D上Zygmund型空间(小Zygmund型空间)之间的广义复合算子的有界性和紧性,得到算子Cφg:Zα→Zβ为有界和紧性的几个充要条件.把结论进一步推广,得到复合算子Cφ:Zα→Zβ为有界和紧性的几个充要条件.第三章研究了单位圆盘D上从Zygmund型空间到Bers型空间的微分算子与加权复合算子的乘积的有界性和紧性,得到了相关的解析函数u和解析自映射Φ所应满足的几个充要条件.第四章研究了单位球中从Zygmund空间到Bloch型空间的复合算子的有界性,运用新的检验函数得到了在单位球上复合算子为有界算子的充要条件并把结果丰富到小Zygmund空间.更多还原

【Abstract】 We mainly study generalized composition operator, product of differential operator and weighted composition operator, composition operator. We use op-erator definitions, some properties of the norm and select test function, obtain necessary and sufficient conditions that these operators are bounded operators or compact operators in different holomorphic function spaces. This thesis consists of4chapters:In the first chapter, we discuss weighted composition operator, generalized composition operator, product of differential operator and weighted composition operator of the research background and give some basic concepts and notations. At last, we show the significance of research work.In the second chapter, the boundedness and compactness of generalized com-position operators on Zygmund type spaces in the unit disk are investigated in this paper. Further, we can get the boundedness and compactness of composition op-erators on Zygmund type spaces in the unit disk.In the third chapter, we study the boundedness and compactness of prod-ucts of differential operator and weighted composition operator on Zygmund type space in the unit disk, to find the conditions that the holomorphic function u and holomorphic self-map φ satisfied.In the fourth chapter, we use a new test function studying composition op- erator from Zygmund space to Bloch type space in the unit ball and obtain the necessary and sufficient conditions for bounded operator.更多还原