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Cobos Díaz, Fernando Kühn, Thomas Sickel, Winfried 2023-06-17T13:19:36Z 2023-06-17T13:19:36Z 2019-02-11 0022-247X 10.1016/j.jmaa.2019.02.027 https://hdl.handle.net/20.500.14352/13083 https://doi.org/10.1016/j.jmaa.2019.02.027 We work with spaces of periodic functions on the d-dimensional torus. We show that estimates for L∞-approximation of Sobolev functions remain valid when we replace L1 by the isotropic periodic Besov space B01;1 or the periodic Besovspace with dominating mixed smoothness S01;1B. For t > 1=2, we also prove estimates for L2-approximation of functions in the Besov space of dominating mixed smoothness St 1;1B, describing exactly the dependence of the involved constants on the dimension d and the smoothness t. eng open access On optimal approximation in periodic Besov spaces journal article