When I read the paper Teichmuller spaces and BMOA by K. Astala and M. Zinsmeister, I am stuck in the following eqution for a long time. $$\iint_\mathbb{D} \bar{\partial}f(z)(\zeta-z)^{-2}\mathrm dx\mathrm dy=\pi (f'(\zeta)-1)$$ where $f=z+\dfrac {b_1}{z}+\cdots$.
It seems the equation is kind of related to Cauchy-Pompeiu’s Formula, but I have no idea how to get that $1$. I think $\bar{\partial}f(z)$ means $\dfrac{\partial f}{\partial\bar z}$, I am not very sure since the author didn't give the definition.
I put the original paper here, obviously the third equation omits a minus. Thanks for your help!
