Estimates of the best orthogonal trigonometric approximations of the classes of convolutions of periodic functions of not high smoothness
DOI:
https://doi.org/10.15407/dopovidi2015.07.013Keywords:
best orthogonal trigonometric approximations, classes of (ψ; β)- differentiable functions, classes of convolutionsAbstract
We obtain order estimates for the best uniform orthogonal trigonometric approximations of 2π-periodic functions, whose (ψ,β)-derivatives belong to unit balls of spaces Lp, 1≤p<∞, in the case where a consequence ψ(k) is such that the product ψ(n)n1/p can tend to zero slower than any power function, and ∑k=1∞ψp′(k)kp′−2<∞, when 1<p<∞, 1/p+1/p′=1 or ∑k=1∞ψ(k)<∞, when p=1. We establish the analogous estimates in theLp′ -metric for the classes of summable (ψ,β)-differentiable functions such that ∥fψβ∥1≤1.
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