  In this article we study commutant lifting, more generally intertwining
lifting, for different reproducing kernel Hilbert spaces over two domains in
$\mathbb{C}^n$, namely the unit ball and the unit polydisc. The reproducing
kernel Hilbert spaces we consider are mainly weighted Bergman spaces. Our
commutant lifting results are explicit in nature and that is why these results
are new even in one variable $(n=1)$ set up.
