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.