Estimates of the best orthogonal trigonometric approximations of the generalized multidimensional analogues of the Bernoulli kernels and classes $L^\psi_{\beta,1}$ in the space $L_q$

• Date: 2016
• Author Affiliations: К. В. Швай — Інститут математики НАН України
• Keywords: keywords
• Main Authors: Shvai, K. V., Швай, К. В.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2016
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/225
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

We obtain order estimates of the best orthogonal trigonometric approximation of the functions $D^\psi_{\beta}$ in the space $L_q$, with $1<q<\infty$. These functions are generalized multidimensional analogs of the Bernoulli kernels. The results obtained are applied to establish...