Estimates of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables with given majorant of mixed moduli of continuity in the space $L_{q}$

Abstract

In this paper, we continue the study of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables whose majorant of the mixed moduli of continuity contains both exponential and logarithmic multipliers. We obtain the exact-order estimates of the orthoprojective widths of the classes $B^{\Omega}_{p,\theta}$ in the space $L_{q},$ $1\leq p<q<\infty,$ and also establish the exact-order estimates of approximation for these classes of functions in the space $L_{q}$ by using linear operators satisfying certain conditions.

Keywords

• orthoprojective width
• mixed modulus of continuity
• linear operator
• vallée-poussin kernel
• fejér kernel