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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2014_96_6_a6,
     author = {R. V. Dallakjan},
     title = {On {Blaschke} {Products} with {Finite} {Dirichlet-Type} {Integral}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {880--884},
     publisher = {mathdoc},
     volume = {96},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a6/}
}
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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/