@article{Serdyuk_Stepanyuk_2014, title={Order Estimates for the Best Approximations and Approximations by Fourier Sums in the Classes of Convolutions of Periodic Functions of Low Smoothness in the Uniform Metric}, volume={66}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2253}, abstractNote={We obtain the exact-order estimates for the best uniform approximations and uniform approximations by Fourier sums in the classes of convolutions of periodic functions from the unit balls of the spaces $L_p, 1 ≤ p < ∞$, with generating kernel $Ψ_{β}$ for which the absolute values of its Fourier coefficients $ψ(k)$ are such that $∑_{k = 1}^{∞} ψ_p ′(k)k^{p ′ − 2} &lt; ∞,\; \frac 1p + \frac 1{p′} = 1$, and the product $ψ(n)n^{1/p}$ cannot tend to zero faster than power functions.}, number={12}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Serdyuk, A. S. and Stepanyuk, T. A.}, year={2014}, month={Dec.}, pages={1658–1675} }