  Let $ \Pi _{b}$ be a bounded $n$ parameter paraproduct with symbol $b$. We
demonstrate that this operator is in the Schatten class $\mathbb S_ p$,
$0<p<\infty$, if the symbol is in the $n$ parameter Besov space $B_p$. Our
result covers both the dyadic and continuous version of the paraproducts in the
multiparameter setting. A direct method of proof is given and an application to
the commutator of the double Hilbert transforms is provided.
