  We study the theta lifting for real unitary groups and completely determine
the theta lifts of discrete series representations. In particular, we show that
these theta lifts can be expressed as cohomologically induced representations
in the weakly fair range. This extends a result of J.-S. Li in the case of
discrete series representations with sufficiently regular infinitesimal
character, whose theta lifts can be expressed as cohomologically induced
representations in the good range.
