Special Toeplitz operators on a class of bounded Hartogs domains

Abstract

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