On optimal approximation in periodic Besov spaces

Cobos Díaz, Fernando; Kühn, Thomas; Sickel, Winfried

On optimal approximation in periodic Besov spaces

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Official URL

https://doi.org/10.1016/j.jmaa.2019.02.027

Publication date

2019

Authors

Cobos Díaz, Fernando

Kühn, Thomas

Sickel, Winfried

Publisher

Elsevier

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URI

https://hdl.handle.net/20.500.14352/13083

Abstract

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.