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In the answers to this question it is proved that if $f:\mathbb{R}\to\mathbb{C}$ is a $\alpha$-Hölder $2\pi$-periodic function, then the Fourier series of $f$ converges uniformly to $f$.

In the answer to this question it is proved that if $f:\mathbb{R}\to\mathbb{C}$ is a continuous bounded variation $2\pi$-periodic function, then the Fourier series of $f$ converges uniformly to $f$.

Note that since the Weierstrass function is $\alpha$-Hölder continuous for every $\alpha<1$ and differentiable nowhere (hence not of bounded variation), and since $x\mapsto\frac{1}{\log(x)}$ is absolutely continuous in $[-\frac{1}{2},\frac{1}{2}]$ but not $\alpha$-Hölder continuous for any $\alpha\in(0,1)$, the first result doesn't imply directly the second and vice versa.

Can be both theorems be viewed as particular results of a theorem for a class of functions that contains both continuous bounded variation periodic functions and $\alpha$-Hölder periodic functions?

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