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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 theirFourier transforms in sets generated by the level surfaces of a function$\Omega$.

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