单位球的Bergman空间上Schatten类加权复合算子

Schatten Class Weighted Composition Operators on the Bergman Space of the Unit Ball

中文关键词:  Bergman空间  加权复合算子  Schatten-类  Hilbert-Schmidt算子.

英文关键词:Bergman space  weighted composition operator  Schatten class  Hilbert-Schmidt operator.

中文摘要:

      本文研究了单位球的Bergman空间上Schatten 类加权复合算子,得到了这种加权复合算子属于Schatten-Von Neumann理想$S_p$的几个充要条件. 作为推论给出了$W_{\varphi, \psi}$是一个Hilbert-Schmidt算子的充要条件是$$\int_{B_n}\frac{|\psi(w)|^2}{(1-|\varphi(w)|^2)^{n+1}}\d V(w)<\infty.$$

英文摘要:

      We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sufficient conditions for such kind of weighted composition operators belong to the Schatten-Von Neumann ideal $S_p$. As a corollary, we now have that $W_{\varphi, \psi}$ is a Hilbert-Schmidt operator if and only if $$\int_{B_n}\frac{|\psi(w)|^2}{(1-|\varphi(w)|^2)^{n+1}}\d V(w)<\infty.$$