Bounded operators on weighted spaces of holomorphic functions on the polydisk

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 $A^p(\omega )$.