On the interpolation in some classes of holomorphic in the unit disk functions

There is considered an interpolation problem f(λₙ )=bₙ in the class of holomorphic in the unit disk U(0;1)= |z|<1 of finite η-type, i.e such that (∃ A>0)(∀ z∈ U(0;1)) |f(z)|≤exp(Aη( A1-|z|)), where η [1;+∞)→ [0;+∞) is an increasing convex function with respect to lnt and lnt=o(η ( t)) (t→+∞).There were received sufficient conditions of the interpolation problem solvability in terms of the counting functions N(r)=∫₀ʳ(n(t)-1)⁺/tdt and Nλₙ (r)=∫₀ʳ(nλₙ(t)-1)⁺tdt. Earlier, in 2004, necessary conditions were obtained (Ukr. Math. J., { 56} (2004), 3) in these terms.For the moderate growth of f (when the majorant η=ψ satisfies the condition ψ(2x)=O(ψ(x)),\ x→+∞) that problem was solved in J. Math. Anal. Appl., { 414} (2014), 1.In this paper, we remove any restrictions on the growth of η and construct an interpolation function f such that(∃ A'>0)(∀ z∈ U(0;1)) |f(z)|≤exp(A'(1-|z|)3/2η(A'/1-|z|)).