Transfer behavior

At intersections, the three pair singularities are added, not multiplied. In particular ${\int }_{|\mathbf{q}|<a}|\mathbf{q}{|}^{-2}{\mathrm{d}}^{3}q=4\pi a$ is the relevant local estimate. A mixed-sign $r^{-2}$ term need not be locally square integrable; the result below is a form theorem.

Figure fig:cubic-transfers organizes the signed kernels, divergence cancellation, and transfer bounds.