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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 L ∞… Click to show full abstract
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 L ∞ by the isotropic periodic Besov space B ∞ , 1 0 or the periodic Besov space with dominating mixed smoothness S ∞ , 1 0 B . For t > 1 / 2 , we also prove estimates for L 2 -approximation of functions in the Besov space of dominating mixed smoothness S 1 , ∞ t B , describing exactly the dependence of the involved constants on the dimension d and the smoothness t.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2019
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