论文标题
对对称域上塑形功能不变空间的调查
A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains
论文作者
论文摘要
我们在对称域上的一类不变空间，包括在其圆界实现中以及其无限的实现中，作为II型Siegel域，它们在对称域上的一类新旧结果。这些空间包括：加权伯格曼空间； Hardy Space $ H^2 $; Dirichlet空间；全态空间； Bloch空间。我们的主要重点将是不变的希尔伯特和半希尔伯特的空间，但我们还将讨论在适当的不变的Banach和Semi-Banach空间中的最小和最大空间。
We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces include: weighted Bergman spaces; the Hardy space $H^2$; the Dirichlet space; holomorphic Besov spaces; the Bloch space. Our main focus will be on invariant Hilbert and semi-Hilbert spaces, but we shall also discuss minimal and maximal spaces in suitable classes of invariant Banach and semi-Banach spaces.
