Некоторые точные нер авенства в теории при ближения функций

Exact inequalities are obtained that illuminate the interrelation between best polynomial approximations of functions, analytic in the disk and the modulus of continuity of the derivatives of the boundary values of these functions.For various classes of functions exact estimates are given for the derivative of a function by means of the modulus of continuity of this function and the modulus of continuity of its second derivative.As application, exact inequalities are deduced, analogous to the well-known Bernstein and Hardy inequalities.