  A bilinear estimate in terms of Bourgain spaces associated with a linearised
Kadomtsev-Petviashvili-type equation on the three-dimensional torus is shown.
As a consequence, time localized linear and bilinear space time estimates for
this equation are obtained. Applications to the local and global well-posedness
of dispersion generalised KP-II equations are discussed. Especially it is
proved that the periodic boundary value problem for the original KP-II equation
is locally well-posed for data in the anisotropic Sobolev spaces
$H^s_xH^{\e}_y(\T^3)$, if $s \ge \frac12$ and $\e > 0$.
