论文标题
在加权希尔伯特空间Dirichlet系列上的作曲操作员
Composition operators on weighted Hilbert spaces of Dirichlet series
论文作者
论文摘要
我们研究了Dirichlet系列的加权希尔伯特空间中特征零的组成算子。为此，我们证明了与Dirichlet系列符号相关的加权平均计数函数的存在，并为组成操作员提供了相应的变量公式更改。这导致了界限和紧凑性的自然必要条件。对于Bergman型空间，我们能够通过使用Schwarz型引理来证明紧凑条件也足够。
We study composition operators of characteristic zero on weighted Hilbert spaces of Dirichlet series. For this purpose we demonstrate the existence of weighted mean counting functions associated with the Dirichlet series symbol, and provide a corresponding change of variables formula for the composition operator. This leads to natural necessary conditions for the boundedness and compactness. For Bergman-type spaces, we are able to show that the compactness condition is also sufficient, by employing a Schwarz-type lemma for Dirichlet series.
