Hyponormal block Toeplitz operators with non-harmonic symbols on the weighted Bergman space

Abstract

In this paper, we discuss hyponormal block Toeplitz operators $T_{\Phi}$ over the vector-valued weighted Bergman space $A_\alpha^2\left(\mathbb{C}^n\right)$. And two conditions about hyponormal block Toeplitz operators $T_{\Phi}$ on $A_\alpha^2\left(\mathbb{C}^n\right)$ were discussed separately, where $ \Phi(z)=A z^p \bar{z}^q + B z^s \bar{z}^t $, $A,B$ are any n-order complex square matrices.