论文标题
$ s^2（\ mathbb {d}）$上的组成分化运算符
Composition-differentiation operators on $S^2(\mathbb{D})$
论文作者
论文摘要
我们调查作用于空间$ s^2 $的组成分化运算符，这是开放单元磁盘上的分析功能的空间，其第一个导数在$ h^2 $中。具体而言，我们确定作用于$ s^p $的有界和紧凑的构图分化操作员的特征。另外，对于特定类别的诱导地图，我们计算标准并确定频谱。最后，对于特定的线性分数诱导地图，我们确定作用在加权伯格曼空间上的组成分化操作员的伴随，其中包括$ s^2，h^2 $和dirichlet空间。
We investigate composition-differentiation operators acting on the space $S^2$, the space of analytic functions on the open unit disk whose first derivative is in $H^2$. Specifically, we determine characterizations for bounded and compact composition-differentiation operators acting on $S^p$. In addition, for particular classes of inducing maps, we compute the norm, and identify the spectrum. Finally, for particular linear fractional inducing maps, we determine the adjoint of the composition-differentiation operator acting on weighted Bergman spaces which include $S^2, H^2$, and the Dirichlet space.
