Toeplitz operators on the $n$-dimensional Hartogs triangle

TL;DR

This paper introduces Toeplitz operators on the Hardy space of the n-dimensional Hartogs triangle, relating them to those on the polydisc and highlighting unique properties of the Hartogs triangle case.

Contribution

It establishes a precise relationship between Toeplitz operators on the Hartogs triangle and the polydisc, and explores their distinct properties.

Findings

Derived properties of Toeplitz operators on the Hartogs triangle from polydisc results.

Identified differences in operator behavior between Hartogs triangle and polydisc cases.

Abstract

We formally introduce and study Toeplitz operators on the Hardy space of the $n$-dimensional Hartogs triangle. We find a precise relation between these operators and the Toeplitz operators on the Hardy space of the unit polydisc $\mathbb D^n.$ As an application, we deduce several properties of these operators from their polydisc counterparts. Furthermore, we show that certain results achieved for the Toeplitz operators on the $n$-dimensional Hartogs triangle are not the same as those in the polydisc case.