A Criterion to determine whether a series is Fourier or not . A example of a function thet satisface Hölder criterion but not Dini.
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Please correct me if I'm wrong, but do you need to know is a series is the Fourier transform of a function? – caverac Nov 23 '16 at 12:36
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If a function satisfies a Holder condition at $x$ with exponent $\alpha > 0$, then it satisfies the Dini condition at $x$ as well. That's an easy check. – Disintegrating By Parts Nov 24 '16 at 15:52