Basic result: let {z_n} be a sequence of points of the unit disc and {k_n} be a sequence of natural numbers, satisfying the conditions:[Figure not available: see fulltext.] Then for any bounded sequence of complex numbers[Figure not available: see fulltext.] there exists a sequence[Figure not available: see fulltext.] such that the function[Figure not available: see fulltext.] interpolates ω: where B_Λ is the Blaschke product with zeros at the points λ_n^(k)}, M is a constant,[Figure not available: see fulltext.]. if N=1 this theorem is proved by Earl (RZhMat, 1972, 1B 163). The idea of the proof, as in Earl, is that if the zeros {λ_n^(k)} run through neighborhoods of the points z_n, then the Blaschke products with these zeros interpolate sequences ω, filling some neighborhood of zero in the space Z^∞. The theorem formulated is used to get interpolation theorems in classes narrower than H^∞.