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 < ∞, \( \frac{1}{p}+\frac{1}{p^{\prime }}=1 \) , and the product ψ(n)n 1/p cannot tend to zero faster than power functions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 12, pp. 1658–1675, December, 2014.
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Serdyuk, A.S., Stepanyuk, T.A. 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. Ukr Math J 66, 1862–1882 (2015). https://doi.org/10.1007/s11253-015-1056-6
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DOI: https://doi.org/10.1007/s11253-015-1056-6