TY - JOUR
AU - A. S. Romanyuk
AU - S. Ya. Yanchenko
PY - 2022/07/07
Y2 - 2022/08/15
TI - Approximation of classes of periodic functions in one and many variables from the Nikol’skii – Besov and Sobolev spaces
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 74
IS - 6
SE - Research articles
DO - 10.37863/umzh.v74i6.7141
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/7141
AB - UDC 517.51In this paper, we obtain exact-order estimates for the best orthogonal trigonometric approximations of the Nikol'skii-Besov classes $B^{\boldsymbol{r}}_{1,\theta}(\mathbb{T}^d),$ $1\leq\theta\leq\infty,$ of periodic functions of one and many variables with dominating mixed smoothness in the space $B_{\infty,1}(\mathbb{T}^d)$.In the multidimensional case, $d\geq 2,$ we establish exact-order estimates for approximations of the mentioned classes of functions by their step-hyperbolic Fourier sums and find the orthoprojection width orders in the same space. The behavior of corresponding approximation characteristics of the Sobolev classes $W^{\boldsymbol{r}}_{1,\boldsymbol{\alpha}}\left(\mathbb{T}^d\right)$ for $d\in\{1,2\}$ is also studied.
ER -