Special Toeplitz operators on a class of bounded Hartogs domains

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