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From: filipovic81 on 9 Sep 2009 00:00
> I have a question regarding the fractional derivative
> of a function f
> defined via multiplication on the fourier side:
>
> D^\alpha f = \F^{-1}((i\omega)^\alpha \F f(\omega)
> ),
>
> \F denoting Fourier transform.
>
> Is it possible to estimate the (say L-infinity-) norm
> of D^\alpha (fg) by
> the maximum of the norms of D^\beta f D^\gamma g over
> all \beta , \gamma <= \alpha?
>
> If \alpha is an integer one can use the product rule
> to get the result trivially
>
> thanks for your answers!

To whom it may concern: the answer is contained in the paper

'dispersion of small amplitude solutions of the generalized kortweg-devries equation' by F.M. Christ and M.I. Weinstein, J. Funct. Anal. 100, 87-109 (1991)

proposition 3.3.

best regards
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