Bergman-Toeplitz operators on fat Hartogs triangles

Abstract

In this paper, we obtain some $L^p$ mapping properties of the Bergman-Toeplitz operator \[ f\longrightarrow T_{K^{-α}}\left(f\right):=\intop_ΩK_Ω\left(\cdot,w\right)K^{-α}\left(w,w\right)f\left(w\right)dV(w) \] on fat Hartogs triangles ${\Omega }_k:=\left\{\left(z_1,z_2\right)\in {\mathbb{C}}^2:{\left|z_1\right|}^k<\left|z_2\right|<1\right\}$, where $\alpha \in \mathbb{R}$ and $k\in {\mathbb{Z}}^{+}$.