lakhmau wrote:
>
>
>
> Dear all,
>
> I would like to know why the (Bessel-like ?) operator which maps
>
> exp(2i.pi.m.x) |-> exp(2i.pi.m.x) / (1 + |m|^2)^{n/2 - 1}
>
> for any multi-index m \in \Z^n maps the space
>
> L^{n/(n-1)}((0,1)^n)
>
> into L^2((0,1)^n) ?
>
> Sorry, the post is not really readable...
>
> Thanks,
> L.

I have an elementary proof of a similar result at the end of the paper:
http://www.math.missouri.edu/~stephen/preprints/thin.html
You may be able to adopt this to your situation. But really, you want
to learn the Littlewood-Paley decomposition and use that.