In there notes you find the following claim (bottom of page 33):
I cannot verify that $D = \mathcal D$. I've drawn them over 5 times now in different ways and I always get the same result:
$D$ is the area below $r=t$ and $\mathcal D$ is the area above $r=t$.
But if this was correct, one cannot exchange an integral over $D$ for one over $\mathcal D$ because any function is not guaranteed to be the same in both areas.
What am I missing?
I need this for the integral in the proof of the Laplace convolution theorem.