Bounded Toeplitz products on the weighted Bergman spaces of the unit ball (Q933497)

The author considers special products of Toeplitz operators of the form \(T_f T_{\overline{g}}\) on the weighted Bergman space \(A_{\alpha}^p\) of the unit ball in \(\mathbb{C}^n\), where \(1\leq p<\infty\), \(\alpha>-1\). Recently, \textit{K.\,Stroethoff} and \textit{D.\,C.\thinspace Zheng} [J.~Math.\ Anal.\ Appl.\ 325, No.\,1, 114--129 (2007; Zbl 1111.32003)] have studied the boundedness and invertibility of such products on the space \(A_{\alpha}^2\) of the ball. In the paper under review, the author extends their results. Also, a different approach is used, which is based on reproducing kernels.