  We consider $k$-dimensional central sections of the unit ball of $\ell_p^n$
(denoted $B_p^n$) and we prove that their volume are bounded by the volume of
$B_p^n$ whenever $1<p<2$ and $1\le k\le (n-1)/2$ or $k=n-1$. We also consider
$0<p<1$ and other cases. We obtain sharp inequalities involving Gamma Function
in order to get these results.
