# Special Toeplitz operators on a class of bounded Hartogs domains

## TL;DR

This paper studies bounded Toeplitz operators with specific symbols on a broad class of Hartogs domains, providing sharp criteria for their boundedness in $L^p-L^q$ spaces, extending previous results.

## Contribution

It introduces a wider class of Hartogs domains and establishes sharp $L^p-L^q$ boundedness criteria for Toeplitz operators with kernel-based symbols, generalizing prior work.

## Key findings

- Derived sharp boundedness criteria for Toeplitz operators.
- Extended classical results to more general Hartogs domains.
- Generalized previous $L^p-L^q$ boundedness conditions.

## Abstract

We introduce a wider class of bounded Hartogs domains, which contains some generalizations of the classical Hartogs triangle. A sharp criteria for the $L^p-L^q$ boundedness of the Toeplitz operator with symbol $K^{-t}$ is obtained on these domains, where $K$ is the Bergman kernel on diagonal and $t\geq 0$. It generalizes the results by Chen and Beberok in the case $1<p<\infty$.