We consider the action of the operator ℒg(z) = (1 - z)(-1)∫ z (1)f(ζ)dζ on a class of "mixed norm" spaces of analytic functions on the unit disk, X = H α,ν (p,q) , defined by the requirement g ∈ X ⇔ r ↦ (1 - r) (α) M p (r, g ((ν))) ∈ L (q) ([0,1], dr/(1 - r)), where 1 ≤ p ≤ ∞, 0 < q ≤ ∞, α > 0, and ν is a nonnegative integer. This class contains Besov spaces, weighted Bergman spaces, Dirichlet...