Geodesic
The order of approximation of continuous functions by certain linear means of their Fourier series
Matematičeskie zametki, Tome 9 (1971) no. 6, pp. 617-627

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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 
@article{MZM_1971_9_6_a1,
     author = {V. A. Baskakov},
     title = {The order of approximation of continuous functions by certain linear means of their {Fourier} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {617--627},
     publisher = {mathdoc},
     volume = {9},
     number = {6},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a1/}
}
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V. A. Baskakov. The order of approximation of continuous functions by certain linear means of their Fourier series. Matematičeskie zametki, Tome 9 (1971) no. 6, pp. 617-627. http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a1/