Origin of term Ahlfors-David regular

To answer the last question, Calderón's problem was a question regarding mapping properties of the Cauchy integral

$$ C_{\Gamma}f(z)=\frac{1}{2\pi i} \int\limits_{\Gamma} \frac{f(\xi)}{\xi-z} d\xi$$

namely, to determine the rectifiable Jordan curves $\Gamma$ for which $C_{\Gamma}$ gives rise to a bounded operator on $L^2(\Gamma)$. This was solved by Guy David in 1984 who showed that $C_{\Gamma}$ is bounded on $L^2(\Gamma)$ precisely when $\Gamma$ satisfies $ \mathcal{H}(\Gamma \cap B(z_{0},r)) \leq Cr$ for every $z_{0}\in\mathbb{C}$, $r>0$ and some constant $C$. This opened up a large study of (what was called then) Ahlfors regularity by David and Semmes. Some of the results of that study are collected in their monograph from the 90's, Analysis of and on Uniformly Rectifiable Sets.

When $q=1$ this condition appears in Ahlfors' famous paper Zur Theorie der Uberlagerungsflache, Acta Math., 65 (1935) for which he was awarded one of the two very first Fields medals. For long time it was known to complex analysts just as the "Ahlfors condition".