it is all in the title : what is $\overline{\partial} \frac{1}{z^2}$ in the sense of distributions ? I remember that $\overline{\partial} \frac{1}{z}$ is a dirac at 0, but I can't seem to find a way to deduce the result for $1/z^2$ from that. I also know that the support of $\overline{\partial} \frac{1}{z^2}$ is included in $\{0 \}$ so it's a dirac or a derivative of dirac. I was unable to find the proof.
EDIT : as pointed out, the question doesn't make sense since $1/z^2$ is not a distribution.