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

Abstract

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 $\alpha ,\beta \ge 0$ 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 $1<p\le q<\infty$, 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 $L^2(\Omega )$.

29 pages