多元盘Bergman空间上可逆的Toeplitz算子乘积

Invertible Toeplitz Operators Products on the Bergman Space of the Polydisk

中文关键词:  Toeplitz算子  Bergman空间  多元盘  可逆H\"{o}lder 不等式.

英文关键词:Toeplitz operators  Bergman space  polydisk  reverse H\"{o}lder inequality.

中文摘要:

      我们利用二元矩形的笛卡尔积和二元笛卡尔积极大函数证明了多元盘Bergman空间上的一个可逆H\"{o}lder 不等式. 接下来,给出了多元盘上以解析的平方可积函数 $f$ 和$g$ 为符号Toeplitz乘积 $T_{f}T{\bar{g}}$ 在$L_a^2({\mathbb{D}}^n)$上是有界可逆的充要条件.

英文摘要:

      We prove a reverse H\"{o}lder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk. Next, we further describe when for which square integrable analytic functions $f$ and $g$ on the polydisk the densely defined products $T_{f}T_{\bar{g}}$ are bounded invertible Toeplitz operators.