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

Using tools from the theory of operator ideals and s  -numbers, we develop a general approach to transfer estimates for L2L2-approximation of Sobolev functions into estimates for L∞L∞-approximation, with precise control of all involved constants. As an illustration, we derive some results for periodic isotropic Sobolev spaces Hs(Td)Hs(Td) and Sobolev spaces of dominating mixed smoothness Hmixs(Td), always equipped with natural norms. Some results for LpLp-approximation (2