Estimation of the Best Linear Approximations for the Classes B p , θ r $$ {B}_{\mathrm{p},\theta}^{\mathrm{r}} $$ and Singular Numbers of the Integral Operators

Abstract

We establish the exact-order estimates for the best bilinear approximations of the Nikol’skii–Besov classes $$ {B}_{\mathrm{p},\theta}^{\mathrm{r}} $$ of periodic functions of several variables. We also determine the orders of singular numbers for the integral operators with kernels from the classes $$ {B}_{\mathrm{p},\theta}^{\mathrm{r}} $$ .