Special Toeplitz operators on a class of bounded Hartogs domains

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 $1<p<\infty$.