View article

We define two spaces Kp, q, α, β and Mp, α of analytic functions in the unit polydisc Un of Cn, closely related to the mixed norm and the Bergman spaces on Un, and for any holomorphic function F in Kp, q, α, β or in Mp, α we consider its restriction to the diagonal, ie, the function in the unit disc U of C defined by DF (z)= F (z,..., z), and prove that the diagonal mapping D maps Kp, q, α, β onto the mixed-norm space Hp, q, β+ q p (| α|+ 2n− 1)(U) and the space Mp, α onto the Bergman space Ap,| α|+ 2n− 1 (U).