论文标题
在加权迪里奇莱特空间上的组成操作员的紧凑差异
Compact differences of composition operators on weighted Dirichlet spaces
论文作者
论文摘要
在这里，我们考虑何时在加权的dirichlet空间$ \ MATHCAL {D}_α$上紧凑两个组成操作员时。具体而言，我们研究了Dirichlet空间$ \ MATHCAL {D} $和$ S^2 $的组成运算符的差异，这是分析功能的空间，其第一个导数为$ H^2 $，然后使用Calderón的复杂插值将结果扩展到一般的加权Dirichlet Space。作为推论，我们考虑磁盘线性分数自图引起的组成算子。
Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\mathcal{D}_α$. Specifically we study differences of composition operators on the Dirichlet space $\mathcal{D}$ and $S^2$, the space of analytic functions whose first derivative is in $H^2$, and then use Calderón's complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.
