Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative
K. V. Pozharska, A. S. Romanyuk, S. Ya. Yanchenko
Abstract
We established exact in order estimates an approximation of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbolα}(\mathbb{T}^d)$ 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 $B_{q,1}(\mathbb{T}^d)$, $1 \leqslant p, q < \infty$.