Relations between upper bounds of absolute values of functions and their higher derivatives

In this paper we consider functionsf(t), – < t < , which are n times continuously differentiable with a given convex modulus of continuity of the n-th derivative. For a certain class of periodic functions we establish a relationship between upper bounds of the absolute values of a function and its n-th derivative.Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 329–338, September, 1973.