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Using tools from the theory of operator ideals and s-numbers, we develop ageneral approach to transfer estimates for $L_2$ -approximation of Sobolevfunctions into estimates for $L_\infty$-approximation, with precise control ofall involved constants. As an illustration, we derive some results for periodicisotropic Sobolev spaces $H^s ({\mathbb T}^d)$ and Sobolev spaces of dominatingmixed smoothness $H^s_{\rm mix} ({\mathbb T}^d)$, always equipped with naturalnorms. Some results for isotropic as well as dominating mixed Besov spaces arealso obtained.

Optimal approximation of multivariate periodic Sobolev functions in the sup-norm