The $\bar{\partial}$ Poincaré lemma is stated in some texts (Griffiths/Harris and Voisin) roughly as follows: the equation $\frac{\partial g}{\partial \bar z}=f$ is locally solvable in a disc $D \subset \mathbb{C}$. (Here $f$ is smooth and $g$ is to be smooth as well.)
Is it solvable globally (on the whole disc)?