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 Cuckovic and McNeal, and Abate, Raissy and Saracco.