Approximation of ψ - Integrals of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II
We investigate the rate of convergence of Fourier series on the classes L^ψ - N in the uniform and integral metrics. The results obtained are extended to the case where the classes L^ψ - N are the classes of convolutions of functions from 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^ψ - N, which are solutions of the Kolmogorov-Nikol’skii problem. In addition, we establish an analog of the well-known Lebesgue inequality., number=3, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Stepanets, O. I., year=1998, month=Mar., pages=388–400