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^{-\alpha}}\left(f\right):=\intop_{\Omega}K_{\Omega}\left(\cdot,w\right)K^{-\alpha}\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 $k\in \mathbb Z^+$.