The deviation of polygonal functions in the Lp metric

The precise value is given of the upper bound of the deviation in the L_p metric (1 < p < ) of a function f(x) in the class H , given by a convex modulus of continuity(t), from its polygonal approximation at the points x_k=k/n (k=0, 1 ...,n).Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 31–37, 1969.I would like to express my appreciation to A. A. Nudel'man for suggesting the problem considered here and for his help.