Abstract
This considers the question of the best one-sided approximation of certain classes of continuous periodic functions by means of trigonometric polynomials of order ≤n-1 in the metric L2πp (1≤p<∞). Precise upper bounds are obtained for the best one-sided approximation of classes of 2π/n-periodic functions Hω,n [having arbitrary prescribed modulus of continuity ω(t)] in the metric L2πp, as well as of classes of 2π-periodic functions Hω [having prescribed modulus of continuity ω(t) with definite limits] in the metric L2π1.
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