双曲的Q_T，s空间及解析函数空间上的算子理论

【作者】 谭杏娟；

【导师】 谭海鸥；

【作者基本信息】 五邑大学 ， 应用数学， 2010， 硕士

【摘要】 1998年伍鹏程在文章《On increasing functions, Bloch functions and normal functions》中研究了Bloch函数和normal函数的判别准则时引入了一个增函数,2001年伍鹏程和乌兰哈斯在此文的基础上于文《Characterizations of QK spaces》中提出了QK空间的概念。至今QK空间及QK型空间是复函数几何理论研究的热点,有很多问题尚未解决。最近,乌兰哈斯和朱克和等人做了很多关于QK空间与其他空间之间复合算子性质的研究,如乌兰哈斯和伍鹏程给出了从Bloch空间到QK空间上复合算子有界性及紧性刻画,程训辉在文《加权Bloch空间到QK空间的复合算子》中讨论了加权Bloch空间(小加权Bloch空间)和QK间的复合算子Cφ的有界性。2009年周江河在文《关于解析QT,s空间》中提出了QT,s空间的概念和研究了这个空间上的包含关系。近年来,双曲函数空间的研究也成为研究热点,2003年李晓南在其硕士论文中提出了双曲Qp空间并就其初等性质进行了初探。本论文主要由四部分组成：第一章与第二章介绍了函数空间及其算子理论的研究背景和一些主要研究成果。第三章将双曲导数与QT,s空间相结合引入了双曲QT,s空间QT,s*,系统研究了该空间的一些基本性质,其中包括利用Carleson测度来对该空间进行刻画。第四章主要研究了单位圆上对数Bloch空间Blog(B0,log)和空间QT,S的复合算子Cφ的有界性和紧性的充分必要条件。第五章主要讨论了从Bloch型空间Bα到加权Bloch型空间Blogβ的Volterra算子的有界性与紧性的充要条件。更多还原

【Abstract】 P.Wu studied the criterion of normal and Bloch functions with a nondecreasing function in the paper On increasing functions,Bloch functions and normal functions in 1998, on the basic of this paper, P.Wu and H.Wulan formally introduce the definition of QK spaces in their paper Characterizations of QK spaces. By now QK spaces also attracts a lot of attentions of many people. At the same time, there is a lot of unsolved problems in this field. Recently, P.Wu and K.Zhu made a lot of research in the properties of Composition Operators between the QK spaces and other spaces. Such as, P.Wu and H.Wulan gave the characterizations of bounded and compact composition operators from Bloch spaces to QK spaces, X.Cheng in the paper Composition operator between the weighted Bloch space and QK space studied the boundedness of the composition operators between weighted bloch space and QK space. J.Zhou in the paper About the analytic QT,s spaces in 2009 formally introduce the definition of QT,s spaces and the inclusion relations in this space. In recent years, Space of hyperbolic functions has become a research focus, X.Li introduce the definition of hyberbolic Qp spaces in his master’s thesis in 2003, and investigate its primary properties.This thesis mainly consite of four parts:Chapter 1 and chapter 2 introduce the background of the Function spaces and operator theory and some main research results.Chapter 3 we have the hyperbolic QT,s space QT,s* by combining the hyperbolic derivative and the classic QT,s space, investigate some basic properties of hyberbolic QT,s space, include use Carleson measure to charactering hyberbolic QT,s space.Chapter 4 mainly discuss the necessary and sufficient condition when the composition operators Cφfrom Blog (B0,log) space to QT,s space are bounded and compact.Chapter 5 mainly discuss the necessary and sufficient conditions when the Volterra Operator from Bloch type analytic function spaces Bαto weighted bloch type analytic function spaces Blogβ are bounded and compact.更多还原