Geodesic
On the boundary behaviour of functions in the Djrbashyan classes $U_\alpha$ and $A_\alpha$
Eurasian mathematical journal, Tome 4 (2013) no. 2, pp. 57-63 
R. V. Dallakyan. On the boundary behaviour of functions in the Djrbashyan classes $U_\alpha$ and $A_\alpha$. Eurasian mathematical journal, Tome 4 (2013) no. 2, pp. 57-63. http://geodesic.mathdoc.fr/item/EMJ_2013_4_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Nevanlinna factorization theorem was essentially extended in a series of papers by M. M. Djrbashyan for classes $A_\alpha$ and $U_\alpha$ introduced by him, see [2], [3]. In this paper we pay particular attention to non vanishing functions $f\in A_\alpha(-1\alpha0)$ and show that for any $\theta$ except at most a set of zero $(1+\alpha)$-capacity we have $|\ln|f(z)||=o((1-|z|)^{1+\alpha})$ as $z\to e^{i\theta}$.

[1] S. A. Apresyan, R. V. Dallakyan, E. P. Aroyan, “A theorem on harmonic functions belonging to the class of M. M. Djrbashyan”, Proceedings of SEUA (Polytechnic), 2:1 (2010), 27–3

[2] M. M. Djrbashyan, Integral transforms and representations of functions in the complex domain, Nauka, Moscow, 1966 (in Russian) | MR

[3] M. M. Djrbashyan, V. S. Zakarian, Classes and boundary properties of functions meromorphic in a circle, Nauka, Moscow, 1993 (in Russian)

[4] A. G. Naftalevich, “On the interpolation of functions of bounded type”, Recordings of Vilnius University, 5 (1956), 5–27 | MR

[5] I. I. Privalov, Boundary properties of analytic functions, Techno-theory lit. ed., Moscow, 1950 | MR | Zbl

[6] V. S. Zakarian, S. V. Madoyan, “On the boundary values of Djrbashyan class $A_\alpha,U_\alpha$”, Doklady NAS Armenia, 79 (1984), 7–9 | MR