Title: Schatten class composition operators on the Hardy space of Dirichlet series and a comparison-type principle Show Chinese title

Title: 施瓦茨类复合算子在狄利克雷级数的哈迪空间上以及一种比较型原理

Abstract: We give necessary and sufficient conditions for a composition operator with Dirichlet series symbol to belong to the Schatten classes $S_p$ of the Hardy space $\mathcal{H}^2$ of Dirichlet series. For $p\geq 2$, these conditions lead to a characterization for the subclass of symbols with bounded imaginary parts. Finally, we establish a comparison-type principle for composition operators. Applying our techniques in conjunction with classical geometric function theory methods, we prove the analogue of the polygonal compactness theorem for $\mathcal{H}^2$ and we give examples of bounded composition operators with Dirichlet series symbols on $\mathcal{H}^p,\,p>0$. Show Chinese abstract

Abstract: 我们给出了具有Dirichlet级数符号的复合算子属于Hardy空间$\mathcal{H}^2$的Schatten类$S_p$的充要条件。对于$p\geq 2$，这些条件导致了具有有界虚部的符号子类的表征。最后，我们建立了复合算子的比较型原理。结合我们的技术与经典的几何函数理论方法，我们证明了$\mathcal{H}^2$的多边形紧性定理的类似结果，并给出了$\mathcal{H}^p,\,p>0$上具有Dirichlet级数符号的有界复合算子的例子。