Approximative characteristics of classes of functions $S^{\Omega}_{p,\theta}B(\mathbb{R}^d)$ with a given majorant of mixed modulus of smoothness

Abstract

We obtain order estimates of approximation of functions from the classes $S^{\Omega}_{p,\theta}B (\mathbb{R}^d)$ in the space $L_q(\mathbb{R}^d)$, $1<p<q<\infty$, by entire functions of exponential type with supports of their Fourier transforms in sets generated by the level surfaces of a function $\Omega$.