Approximation characteristics of the Nikol’skii-Besov-type classes of periodic functions of several variables in the space B_q,1 - Fedunyk-Yaremchuk, O.V.; Hembars'ka, S.B.; Romanyuk, I.A.; Zaderei, P.V. (Carpathian Mathematical Publications, 2024)
We obtained the exact order estimates of approximation of periodic functions of several variables from the Nikol'skii-Besov-type classes B^Ω_p,θ by using their step hyperbolic Fourier sums in the space B_q,1. The norm in this space is stronger than the L_q-norm. In the considered situations, approximations by the mentioned Fourier sums realize the orders of the best approximations by polynomials with "numbers" of harmonics from the step hyperbolic cross. We also established the exact order estimates of the Kolmogorov, linear and trigonometric widths of classes B^Ω_p,θ in the space B_q,1 for certain relations between the parameters p and q.