Let μ be a finite positive measure on the unit disk and let j ⩾ 1 be an integer. D. Suárez (2015) gave some conditions for a generalized Toeplitz operator \(T_\mu ^{(j)}\) to be bounded or compact. We first give a necessary and sufficient condition for \(T_\mu ^{(j)}\) to be in the Schatten p-class for 1 ⩽ p < ∞ on the Bergman space A², and then give a sufficient condition for \(T_\mu ^{(j)}\) to be in the Schatten p-class (0 < p < 1) on A². We also discuss the generalized Toeplitz operators with general bounded symbols. If ϕ ∈ L^∞ (D, dA) and 1 < p < ∞, we define the generalized Toeplitz operator \(T_\varphi ^{(j)}\) on the Bergman space A^p and characterize the compactness of the finite sum of operators of the form \(T_{{\varphi _1}}^{(j)} \ldots T_{{\varphi _n}}^{(j)}\).

设μ为单位圆盘上的有限正测度，设j ⩾ 1 为整数。D. Suárez (2015) 给出了广义 Toeplitz 算子\(T_\mu ^{(j)}\)有界或紧凑的一些条件。我们首先给出\(T_\mu ^{(j)}\)在 Bergman 空间A ²上1 ⩽ p < ∞属于 Schatten p类的充分必要条件，然后给出一个充分条件\(T_\mu ^{(j)}\ ) 在A ²上属于 Schatten p级 (0 < p < 1) 。我们还讨论了具有一般有界符号的广义 Toeplitz 算子。如果ϕ ∈ L ^∞ ( D , d A)和 1 < p < ∞，我们在 Bergman 空间A ^p上定义广义 Toeplitz 算子\(T_\varphi ^{(j)}\)并刻画有限和的紧致性形式的运算符\(T_{{\varphi _1}}^{(j)} \ldots T_{{\varphi _n}}^{(j)}\)。