  We reconsider generalizations of Hardy's inequality corresponding to the case
of (point) dipole potentials $V_{\gamma}(x) = \gamma (u, x) |x|^{-3}$, $x \in
\mathbb{R}^n \backslash \{0\}$, $\gamma \in [0,\infty)$, $u \in \mathbb{R}^n$,
$|u|=1$, $n \in \mathbb{N}$, $n \geq 3$. More precisely, for $n \geq 3$, we
provide an alternative proof of the existence of a critical dipole coupling
constant $\gamma_{c,n} > 0$, such that \begin{align*} &\text{for all $\gamma
\in [0,\gamma_{c,n}]$, and all $u \in \mathbb{R}^n$, $|u|=1$,} \\ &\quad
\int_{\mathbb{R}^n} d^n x \, |(\nabla f)(x)|^2 \geq \pm \gamma
\int_{\mathbb{R}^n} d^n x \, (u, x) |x|^{-3} |f(x)|^2, \quad f \in
D^1(\mathbb{R}^n). \end{align*} with $D^1(\mathbb{R}^n)$ denoting the
completion of $C_0^{\infty}(\mathbb{R}^n)$ with respect to the norm induced by
the gradient. Here $\gamma_{c,n}$ is sharp, that is, the largest possible such
constant, and we discuss a numerical scheme for its computation. Moreover, we
discuss upper and lower bounds for $\gamma_{c,n} > 0$.
  We also consider the case of multicenter dipole interactions with dipoles
centered on an infinite discrete set.
