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arXiv:2410.12448 [math.CA]AbstractReferencesReviewsResources

Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative

K. V. Pozharska, A. S. Romanyuk, S. Ya. Yanchenko

Published 2024-10-16Version 1

We established exact in order estimates an approximation of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}(\mathbb{T}^d)$ of periodic functions of many variables with a bounded dominating mixed derivative. The approximation is made using trigonometric polynomials with the spectrum in step-hyperbolic crosses, and the error is estimated in the metric of the space $B_{q,1}(\mathbb{T}^d)$, $1 \leqslant p, q < \infty$.

Comments: 18 pages, in Ukrainian
Journal: Ukrainskyi Matematychnyi Zhurnal, Vol. 76, no. 7, Aug. 2024, pp. 1007-1023
Categories: math.CA
Subjects: 41A46, 42A10, 41A50
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