Approximation by step-hyperbolic Fourier sums of classes $\mathbf{MB}^{\omega}_{1,\theta}(\bar{\gamma})$

Abstract

We obtained the exact order estimates of approximation by step-hyperbolic Fourier sums of classes $\mathbf{MB}_{1,\theta}^{\omega}(\bar{\gamma})$ of periodic functions of many variables in the $L_q$-metric $(1<q<\infty)$