On Blaschke Products with Finite Dirichlet-Type Integral

The class of functions with finite Dirichlet-type integral is defined as the set of holomorphic functions $f$ in the unit disk satisfying the following condition:
$$ \int_{0}^{2\pi}\int_{0}^{1} (1-r)^{\alpha}|f'(re^{i\theta})|^{p} r\,dr\,d\theta,\qquad \alpha>-1,\quad 0<p<+\infty. $$
These classes are usually denoted by $D_{\alpha}^p$. In this paper, we prove the converse of Rudin's theorem and thus provide a necessary and sufficient condition for a Blaschke product to belong to the class $D_{0}^{1}$.