  In this paper we study the fifth order Kadomtsev--Petviashvili II (KP--II)
equation on the upper half-plane $U=\{(x,y)\in \R^2: y>0\}$. In particular we
obtain low regularity local well-posedness using the restricted norm method of
Bourgain and the Fourier-Laplace method of solving initial and boundary value
problems. Moreover we prove that the nonlinear part of the solution is in a
smoother space than the initial data.
