TWO-SIDED ESTIMATES FOR SOME FUNCTIONALS IN TERMS OF THE BEST APPROXIMATIONS

摘要

Let C be the space of continuous 2π -periodic functions. For some integrals of the form ∫~π_0 w_r(f, t)Ф(t)dt, where w_r(f,t) is the modulus of continuity of order r of a function f in C, two-sided bounds in terms of the best approximations by trigonometric polynomials are established. Bibliography: 14 titles.