Advanced Search

For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space $H^{p,q,\alpha }\left(Uⁿ\right)$ of the polydisc onto the mixed norm space $H^{p,q,\left|\alpha \right|+(p/q+1)(n-1)}\left(U\right)$ of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.