Q curvature prescription; forbidden functions and the GJMS null space

On an even conformal manifold $(M,c)$, such that the critical GJMS operator has non-trivial kernel, we identify and discuss the role of a finite dimensional vector space $N(Q)$ of functions determined by the conformal structure. Using these we describe an infinite dimensional class of functions that cannot be the Q-curvature $Q^g$ for any $g$ in $c$. If certain functions arise in $N(Q)$ then $Q^g$ cannot be constant for any $g$ in $c$.