Geodesic
Approximation of differentiable functions by partial sums of their Fourier series
Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 291-300.

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For the classes of differentiable functions $W_\alpha^r$, $r>0$, which include the classes of functions which have derivatives $f^{(r)}$ or $\tilde{f}^{(r)}$ with moduli bounded by one, we obtain an asymptotic formula for the supremum of the difference between a function and the partial sums of its Fourier series. The remainder term in our formula is $Cn^{-r}$, in which $C$ is a constant. 
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     author = {S. A. Telyakovskii},
     title = {Approximation of differentiable functions by partial sums of their {Fourier} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {291--300},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a4/}
}
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S. A. Telyakovskii. Approximation of differentiable functions by partial sums of their Fourier series. Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 291-300. http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a4/