The inclusion of certain classes of functions

For any sequence {N_k} with {N_k} O we find sharp theorems on the inclusion of the classes {f: f l (0, 2),e _k ⁽¹⁾ (f) = O(N_k)¦, whereE _k ⁽¹⁾ (f) is the best approximation (in L) of f by trigonometric polynomials of order no greater than k, in the classL with slowly growing and in the class Lv, 1 <v < .Translated from Matematicheskie Zametki, Vol. 20, No. 6, pp. 835–841, December, 1976.