  We generalize the hierarchical equations of motion method to study electron
transport through a quantum dot or molecule coupled to one-dimensional
interacting leads that can be described as Luttinger liquids. Such leads can be
realized, for example, by quantum wires or fractional quantum Hall edge states.
In comparison to noninteracting metallic leads, Luttinger liquid leads involve
many-body correlations and the single-particle tunneling density of states
shows a power-law singularity at the chemical potential. Using the generalized
hierarchical equations of motion method, we assess the importance of the
singularity and the next-to-leading order many-body correlations. To this end,
we compare numerically converged results with second and first-order results of
the hybridization expansion that is inherent to our method. As a test case, we
study transport through a single-level quantum dot or molecule that can be
described by an Anderson impurity model. Cotunneling effects turn out to be
most pronounced for attractive interactions in the leads or repulsive ones if
an excitonic coupling between the dot and the leads is realized. We also find
that an interaction-induced negative differential conductance near the Coulomb
blockade thresholds is slightly suppressed as compared to a first-order and/or
rate equation result. Moreover, we find that the two-particle ($n$-particle)
correlations enter as a second-order ($n$-order) effect and are, thus, not very
pronounced at the high temperatures and parameters that we consider.
