  We investigate the well-posedness in the generalized Hartree equation $iu_t +
\Delta u + (|x|^{-(N-\gamma)} \ast |u|^p)|u|^{p-2}u=0$, $x \in \mathbb{R}^N$,
$0<\gamma<N$, for low powers of nonlinearity, $p<2$. We establish the local
well-posedness for a class of data in weighted Sobolev spaces, following ideas
of Cazenave and Naumkin [6]. This crucially relies on the boundedness of the
Riesz transform in weighted Lebesgue spaces. As a consequence, we obtain a
class of data that exists globally, moreover, scatters in positive time.
Furthermore, in the focusing case in the $L^2$-supercritical setting we obtain
a subset of locally well-posed data with positive energy, which blows up in
finite time.
