  The present paper is the natural evolution of arXiv:1308.3606. For $s>-1$ we
compare two natural types of fractional Laplacians $(-\Delta)^s$, namely, the
"Navier" and the "Dirichlet" ones. As a main tool, we give the "dual"
Caffarelli--Silvestre and Stinga--Torrea variational characterizations of these
operators for $s\in(-1,0)$.
