Toeplitz operators with BMO symbols on the weighted Bergman space of the unit ball (Q644641)

The authors study Toeplitz operators \(T_f\) with \(BMO^1_{\alpha}\)-symbols acting on the standard weighted Bergman spaces \(A^2_{\alpha}(B_n)\), \(\alpha \in (-1, \infty)\), over the unit ball \(B_n\) in \(\mathbb{C}^n\). The main result states that the Toeplitz operator \(T_f\) is bounded if and only if the Berezin transform \(\widetilde{f}\) of its symbol \(f\) is bounded, and \(T_f\) is compact if and only if \(\widetilde{f} \to 0\) as \(z \to \partial B_n\).