On interpolation sequences of one class of functions analytic in the unit disk

We establish a criterion for the existence of a solution of the interpolation problem f(λn) = bn in the class of functions / analytic in the unit disk and satisfying the relation (∃τ1 ∈ (0;1)) (∃C1>0) (∀z,|z|<l): |f(z)| ≤ exp (c1γτ1(c1/1-|z|)), where γ: [l; + ∞)→(0; + ∞) is an increasing function such that the function ln γ(t) is convex with respect to In; on the interval [1; + ∞) and In; = o(ln γ(t)), t→∞. © 2001 Plenum Publishing Corporation.