Approximation of $\bar {ψ} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II - Stepanets, O. I. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We investigate the rate of convergence of Fourier series on the classes $L^{\bar {ψ}} - \text{N}$ in the uniform and integral metrics. The results obtained are extended to the case where the classes $L^{\bar {ψ}} - \text{N}$ are the classes of convolutions of functions from $\text{N}$ with kernels with slowly decreasing coefficients. In particular, we obtain asymptotic equalities for the upper bounds of deviations of the Fourier sums on the sets $L^{\bar {ψ}} - \text{N}$, which are solutions of the Kolmogorov-Nikol’skii problem. In addition, we establish an analog of the well-known Lebesgue inequality.