@article{Serdyuk_Stepanyuk_2015, title={Order Estimates for the Best Orthogonal Trigonometric Approximations of the Classes of Convolutions of Periodic Functions of Low Smoothness}, volume={67}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2033}, abstractNote={We establish order estimates for the best uniform orthogonal trigonometric approximations on the classes of $2π$-periodic functions whose $(ψ, β)$-derivatives belong to unit balls in the spaces $L_p,\; 1 ≤ p < ∞$, in the case where the sequence $ψ(k)$ is such that the product $ψ(n)n^{1/p}$ may tend to zero slower than any power function and $∑^{∞}_{k=1} ψ^{p′}(k)k^{p′−2} < ∞$ for $1 < p < ∞,\; 1\p+1\p′ = 1$, or $∑^{∞}_{k=1} ψ(k) < ∞$ for $p = 1$. Similar estimates are also established in the $L_s$-metrics, $1 &lt; s ≤ ∞$, for the classes of summable $(ψ, β)$-differentiable functions such that $‖f_{β}^{ψ} ‖1 ≤ 1$.}, number={7}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Serdyuk, A. S. and Stepanyuk, T. A.}, year={2015}, month={Jul.}, pages={916–936} }