Bergman-Toeplitz operators between weighted $L^p$-spaces on weakly pseudoconvex domains

In this paper we study the Bergman-Toeplitz operator $T_{\psi }$ induced by $\psi (w)=K_{\mathrm{\Omega }}^{-\alpha }(w,w)d_{\mathrm{\Omega }}^{\beta }(w)$ with $\alpha, \beta \geq 0$actingfromaweighted$L^p$-space$L_a^p(\Omega)$toanotherone$L_a^q(\Omega)$ on a large class of pseudoconvex domains of finite type. In the case $1<p\le q<\mathrm{\infty }$, 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 $L^2(\mathrm{\Omega })$.