Bergman-Toeplitz operators on weakly pseudoconvex domains

Abstract

We prove that for certain classes of pseudoconvex domains of finite type, the Bergman-Toeplitz operator $T_{\psi }$ with symbol $\psi =K^{-\alpha }$ maps from $L^p$ to $L^q$ continuously with $1<p\le q<\infty$ if and only if $\alpha \ge \frac{1}{p}-\frac{1}{q}$, where $K$ is the Bergman kernel on diagonal. This work generalises the results on strongly pseudoconvex domains by Čučković and McNeal, and Abeta, Raissy and Saracco.

18 pages