  We consider the weighted $A^p(\omega)$ and $B_p(\omega)$ spaces of
holomorphic functions on the polydisk (in the case of $p>1$).
  We prove some theorems about the boundedness of Toeplitz operators on
weighted Besov spaces $B_p(\omega)$ and about the boundedness of generalized
little Hankel and Berezin- type operators on $A^p(\omega)$.
