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Aug 20, 2016 at 15:36 comment added Christian Remling @PabloShmerkin: Yes, you're right of course, that was obvious in fact.
Aug 20, 2016 at 13:16 comment added Pablo Shmerkin @ChristianRemling - $\widehat{\mu}$ is Lipschitz, so in this case it is true that if it doesn't go to $0$ then it is in no $L^p$, added edit explaining this.
Aug 20, 2016 at 13:15 history edited Pablo Shmerkin CC BY-SA 3.0
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Aug 19, 2016 at 15:43 history edited Pablo Shmerkin CC BY-SA 3.0
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Aug 19, 2016 at 15:37 comment added Pablo Shmerkin @Denis Serre - thanks, it was a typo, $\phi$ has to be strictly convex, not strictly increasing.
Aug 19, 2016 at 15:37 history edited Pablo Shmerkin CC BY-SA 3.0
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Aug 19, 2016 at 15:35 comment added Denis Serre I don't understand: one can take $\phi$ the identity, and then $\widehat{\phi^*\mu}=\hat\mu$ does not decay.
Aug 19, 2016 at 15:24 history answered Pablo Shmerkin CC BY-SA 3.0