Approximation of differentiable functions by partial sums of their Fourier series

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.