Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative - Pozharska, K.; Romanyuk , A.; Yanchenko, S. (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 517.51We establish exact order estimates for approximations of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbol{α}}(\mathbb{T}^d)$ of periodic functions of many variables with bounded dominant mixed derivative. The approximation is performed by using trigonometric polynomials with spectra in step hyperbolic crosses, and the error is estimated in the metric of the space $B_{q,1}(\mathbb{T}^d),$ $1 ≤ p, q < ∞.$