Geodesic
On angular boundary limits of normal subharmonic functions
Eurasian mathematical journal, Tome 4 (2013) no. 2, pp. 49-56.

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

The paper considers normal subharmonic functions defined in the unit circle. New necessary and sufficient conditions for the existence of angular limits at arbitrary points of the unit circumference are obtained. The obtained conditions are less strong than in the previous results of different authors. Examples confirming the significance of these conditions are given. 
@article{EMJ_2013_4_2_a2,
     author = {S. Berberyan},
     title = {On angular boundary limits of normal subharmonic functions},
     journal = {Eurasian mathematical journal},
     pages = {49--56},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2013_4_2_a2/}
}
TY  - JOUR
AU  - S. Berberyan
TI  - On angular boundary limits of normal subharmonic functions
JO  - Eurasian mathematical journal
PY  - 2013
SP  - 49
EP  - 56
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2013_4_2_a2/
LA  - en
ID  - EMJ_2013_4_2_a2
ER  - 
%0 Journal Article
%A S. Berberyan
%T On angular boundary limits of normal subharmonic functions
%J Eurasian mathematical journal
%D 2013
%P 49-56
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2013_4_2_a2/
%G en
%F EMJ_2013_4_2_a2
S. Berberyan. On angular boundary limits of normal subharmonic functions. Eurasian mathematical journal, Tome 4 (2013) no. 2, pp. 49-56. http://geodesic.mathdoc.fr/item/EMJ_2013_4_2_a2/

[1] F. Bagemihl, W. Seidel, “Sequential and continuous limits of meromorphic functions”, Annal. Acad. Scien. Fennicae, ser. A, 280 (1960), 1–17 | MR

[2] S. L. Berberyan, “On boundary properties of subharmonic functions generating the normal families in the subgroups of automorphisms of the unit circle”, Izvestiya AN ArmSSR, Matematika, 15:4 (1980), 395–402 (in Russian) | MR | Zbl

[3] S. L. Berberyan, “A classification of boundary singularities of normal subharmonic functions and its applications”, Uspekhi Mat. Nauk, 62:3 (2007), 207–208 (in Russian) | DOI | MR | Zbl

[4] S. L. Berberyan, “On angular boundary values of subharmonic functions from the class $N$”, Mathematica Montisnigri, 20–21 (2007–2008), 5–14 | MR | Zbl

[5] S. L. Berberyan, “On angular boundary values of normal continuous functions”, Izvestiya Vuzov, Matematika, 1986, no. 3, 22–28 | MR | Zbl

[6] E. F. Collingwood, A. J. Lohwater, The theory of cluster sets, Cambridge Univ. Press, Cambridge, 1966 | MR | Zbl

[7] V. I. Gavrilov, “Normal functions and almost periodic functions”, Doklady AN USSR, 240:4 (1978), 768–770 (in Russian) | MR | Zbl

[8] V. I. Gavrilov, V. S. Zakaryan, A. V. Subbotin, “Linear-topologic properties of maximal Hardy spaces of harmonic functions in the circle”, Doklady AN Armenii, 102:3 (2002), 203–209 (in Russian) | MR

[9] P. Lappan, “Some results on harmonic normal functions”, Math. Zeitschr., 90:1 (1965), 155–159 | DOI | MR | Zbl

[10] P. Lappan, “Fatous points of harmonic normal functions and uniformly normal functions”, Math. Zeitschr., 102:3 (1967), 110–114 | DOI | MR | Zbl

[11] A. J. Lohwater, “Boundary behaviour of analytic functions”, Itogi Nauki i Tekh., Matem. Analiz, 10, VINITI, 1973, 99–259 (in Russian) | MR | Zbl

[12] S. M. Lozinski, “On subharmonic functions and their applications to surface theory”, Izvestiya AN USSR, ser. Matem., 8:4 (1944), 175–194 (in Russian) | MR | Zbl

[13] J. Meek, “Subharmonic versions of Fatous theorem”, Proc. Amer. Math. Soc., 30:2 (1973), 313–317 | MR

[14] J. Meek, “On Fatous points of normal harmonic functions”, Math. Japonica, 22:3 (1971), 309–314 | MR

[15] D. C. Rung, “Asymptotic values of normal subharmonic functions”, Math. Zeitschr., 84:1 (1964), 9–15 | DOI | MR | Zbl

[16] M. Tsuji, Potential theory of modern function theory, Maruzen, Tokyo, 1959 | MR | Zbl