Geodesic
On Blaschke Products with Finite Dirichlet-Type Integral
Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 880-884.

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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

+\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 $D_{0}^{1}$.
Keywords: Blaschke product, Dirichlet-type integral, Hardy class, holomorphic function. 
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R. V. Dallakjan. On Blaschke Products with Finite Dirichlet-Type Integral. Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 880-884. http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a6/

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