For any holomorphic function f on the unit polydisk D n we consider its restriction to the diagonal, i.e., the function in the unit disc D ⊂ C defined by Diag f(z) = f(z, . . . , z), and prove that the diagonal map Diag maps the space Qp,q,s(D n ) of the polydisk onto the space Qbq p,s,n(D ) of the unit disk.