  For a map of the unit interval with an indifferent fixed point, we prove an
upper bound for the variance of all observables of $n$ variables
$K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on
coupling and decay of correlation properties of the map. We then give various
applications of this inequality to the almost-sure central limit theorem, the
kernel density estimation, the empirical measure and the periodogram.
