Given $g\in\mathcal{C}^1(\bar\Delta)$, and $z\in\Delta$, how can i prove that the 2-form $$ d\omega=\frac{\partial_{\bar{\zeta}}g(\zeta)}{\zeta-z}d\zeta\wedge d\bar{\zeta} $$ is integrable in $z$?
At MSE no one could help me, I hope to be more lucky here.
If you need more detail look at https://math.stackexchange.com/questions/1240685/detail-about-integration-in-cauchy-integral-formula many thanks