  We prove sharp embedding inequalities for certain reduced Sobolev spaces that
arise naturally in the context of Dirichlet problems with $L^1$ data. We also
find the optimal target spaces for such embeddings, which in dimension 2 could
be considered as limiting cases of the Hansson-Brezis-Wainger spaces, for the
optimal embeddings of borderline Sobolev spaces $W_0^{k,n/k}$.
