单位球加权伯格曼空间上托普里兹算子的乘积

Products of Toeplitz Operator on the Weighted Bergman Space of the Unit Ball

中文关键词:  托普里兹算子  伯格曼空间  单位球  Hankel算子.

英文关键词:Toeplitz operator  Bergman space  unit ball  Hankel operator.

中文摘要:

      本文主要研究了单位球加权伯格曼空间上托普里兹算子乘积$T_{f}T_{\bar{g}}$有界可逆性及有界Fredholm性的充分条件和必要条件, 其中$f$,$g$为平方可积解析函数. 并且给出了混合乘积$H_{f}T_{\bar{g}}$有界性的充分条件和必要条件, 其中$f\in L^{2}(B_{n}, dv_{\alpha})$, $g$为平方可积解析函数.

英文摘要:

      We consider the question for what kind of square integrable holomorphic functions $f$, $g$ on the unit ball the densely defined products $T_{f}T_{\bar{g}}$ are invertible and Fredholm on the weighted Bergman space of the unit ball. We furthermore obtain necessary and sufficient conditions for bounded Haplitz products $H_{f}T_{\bar{g}}$, where $f\in L^{2}(B_{n}, \d v_{\alpha})$ and $g$ is a square integrable holomorphic function.