Are there an results on functions annihilated by the n-times iterated Cauchy-Riemann operator ${\partial\over\partial\bar z}$, aka functions $f$ that for some $n\in\mathbb{N}$ satisfy the following equation?
$${\partial^n f\over\partial\bar z^n}=0$$
EDIT: I have posted the same questions only a very short period of time ago, when my web browser suddenly froze and I didn't believe the question got posted successively, therefor posting it again here. If such repetition goes against any site rules or regulations, as I would suspect it does, may somebody in power to do so please remove one of the posts. Thank you!



n-times iterated Cauchy-Riemann operator
You can prove by induction that, if $f$ satisfies your equation, then there exist holomorphic functions $f\_0,\ldots,f\_{n-1}$ on the domain of $f$ such that
$$
f = f\_0(z) + f\_1(z)\ \bar z + \cdots + f\_{n-1}(z)\ {\bar z}^{n-1}.
$$
Is this the kind of answer you had in mind?


