$L^p$ Regularity of Toeplitz Operators on Generalized Hartogs Triangles

Abstract

We obtain $L^p$ estimates for Toeplitz operators on the generalized Hartogs triangles ${\mathbb{H}}_{\gamma }=\{(z_1,z_2)\in {\mathbb{C}}^2:|z_1{|}^{\gamma }<|z_2|<1\}$ for two classes of positive radial symbols, one a power of the distance to the origin, and the other a power of the distance to the boundary.

13 pages