I saw the following theorem in the wiki page:
<http://en.wikipedia.org/wiki/H%C3%B6lder_condition>




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if $f$ satisfies the $\alpha$-Hölder condition 
$| f(x) - f(y) | \leq C \, |x - y|^{\alpha}$ for some $\alpha>1/2$,
then 


$||f||\_{A} = \sum\_i |c\_{i}|\leq C c\_{\alpha}$


where $c\_{\alpha}$ only depends on $\alpha$




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But I could not find a reference or a proof for this theorem. 
Can anybody provide me a ref for this? Thanks a lot!



absolute convergence of the Fourier coeff for Hölder continuous function
The proof is outlined in Stein-Shakarchi's book Fourier Analysis, Chapter 3, Exercise 16. 


