Spaces of Holomorphic Functions in the Unit Ball
Spaces of Holomorphic Functions in the Unit Ball
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DOI：
10.1007/0-387-27539-8
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Kehe Zhu
中科院分区：
文献类型：
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作者：
Kehe Zhu
近年来，在定义松散的全纯空间领域出现了一系列的研究活动。本书讨论了C^ n单位球中最著名和应用最广泛的全纯函数空间。讨论的空间包括Bergman空间、Hardy空间、Bloch空间、BMOA空间、Dirichlet空间、Besov空间和Lipschitz空间。书中的大多数校样都是新的，比文献中现有的校样更简单。几乎所有这些证明的中心思想都是基于全纯函数的积分表示和Bergman核、Bergman度规和自同构群的初等性质。选择单位球作为设置，因为使用简单的公式可以获得大多数结果，而不会有太多的麻烦。任何熟悉单变量复分析的人都可以轻松地阅读这本书；不需要几个复杂变量的先决条件。作者在每一章的末尾都有不同难度的练习。
There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^ n. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing ones in the literature. The central idea in almost all these proofs is based on integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group.The unit ball was chosen as the setting since most results can be achieved there using straightforward formulas without much fuss. The book can be read comfortably by anyone familiar with single variable complex analysis; no prerequisite on several complex variables is required. The author has included exercises at the end of each chapter that vary greatly in the level of difficulty.