  In a recent article, we studied the global solvability of the so-called
cohomological equation L_X f=g in C^\infty(\Rt), where X is a regular vector
field on the plane and L_X the corresponding Lie derivative. In a joint article
with T. Gramchev and A. Kirilov, we studied the existence of global L^1_{loc}
weak solutions of the cohomological equation for vector fields depending only
on one coordinate. Here we generalize the results of both articles by providing
explicit conditions for the existence of global weak solutions to the
cohomological equation when X is intrinsically Hamiltonian or of finite type.
