On the Best Polynomial Approximation in Hardy Space

Sharp Jackson-Stechkin-type inequalities, in which the best polynomial approximation of a function in the Hardy space is estimated from above, both in terms of the generalized modulus H-2 of continuity of the mth order and in terms of the K-functional of rth derivatives, are found. For some classes of functions defined with the formulated characteristics in the space, the exact values of H-2 n widths are calculated. Also in the classes W-2((r))((omega) over tilde (m), Phi) and W-2((r))(K-m, Phi), where r is an element of N and r >= 2, the exact values of the best polynomial approximations of intermediate derivatives f((s)), 1 <= s <= r -1 are obtained.