  We present a generalized version of holographic dark energy arguing that it
must be considered in the maximally subspace of a cosmological model. In the
context of brane cosmology it leads to a bulk holographic dark energy which
transfers its holographic nature to the effective 4D dark energy. As an
application we use a single-brane model and we show that in the low energy
limit the behavior of the effective holographic dark energy coincides with that
predicted by conventional 4D calculations. However, a finite bulk can lead to
radically different results.
