The deviation of polygonal functions in the $L_p$ metric

The precise value is given of the upper bound of the deviation in the $L_p$ metric $(1\le p<\infty)$ of a function $f(x)$ in the class $H_\omega$, given by a convex modulus of continuity $\omega(t)$, from its polygonal approximation at the points $x_k=k/n$ ($k=0,1,\dots,n$).