In this paper we study the Bergman-Toeplitz operator $T_{ \psi}$ induced by $\psi(w) = K_{ \Omega}^{ -\alpha}(w,w)d_{ \Omega}^{ \beta}(w)$ with $\alpha, \beta \geq 0$ acting from a weighted $L^p$-space $L_a^p(\Omega)$ to another one $L_a^q(\Omega)$ on a large class of pseudoconvex domains of finite type. In the case $1 < p \leq q < \infty$, the following results are established: \\ - Necessary and sufficient conditions for boundedness, which generalize the recent results obtained by Khanh, Liu and Thuc.\\ - Upper and lower estimates for essential norm, in particular, a criterion for compactness.\\ - A characterization of Schatten class membership of this operator on Hilbert space $L^2(\Omega)$.
Categories: math.CV math.FA