The order of approximation of continuous functions by certain linear means of their Fourier series

V. A. Baskakov

Matematičeskie zametki, Tome 9 (1971) no. 6, pp. 617-627.

Résumé

The exact order of the quantity $$A_n(\mathfrak M)=\sup_{\Lambda\in\Lambda^*}\sup_{f\in\mathfrak M}\max_x|L_n(f;x;\Lambda)-f(x)|$$ is determined, where $\Lambda^*$ is the class of linear methods of summation of Fourier series $L_n(f;x;\Lambda)$, satisfying $$(n+1)^{p-1}\sum_{k=0}^n|\Delta\lambda_k^{(n)}|^p\leqslant K^*,\quad p>1$$ and $\mathfrak M$ is either the set of continuous functions $H(\omega)$ or $C(F)$. In