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


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 $\alpha$


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

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What is the $A$ norm and what are the $c_i$s? –  Willie Wong Dec 6 '10 at 22:43
    
Have you tried Katznelson's book? –  Yemon Choi Dec 7 '10 at 3:20
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1 Answer

up vote 3 down vote accepted

The proof is outlined in Stein-Shakarchi's book Fourier Analysis, Chapter 3, Exercise 16.

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