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

TL;DR

This paper establishes $L^p$ bounds for Toeplitz operators on generalized Hartogs triangles with specific radial symbols, advancing understanding of their regularity properties in complex analysis.

Contribution

It provides new $L^p$ estimates for Toeplitz operators on generalized Hartogs triangles with particular radial symbols, extending previous results in complex analysis.

Findings

$L^p$ estimates for Toeplitz operators on $ ext{Hartogs}_ ext{triangles}$

Results for symbols as powers of distance to origin or boundary

Enhanced understanding of operator regularity in complex domains

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.