Geodesic
Boundary properties of subclasses of meromorphic functions of
Izvestiya. Mathematics, Tome 4 (1970) no. 6, pp. 1273-1354 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

One of the authors [1] has constructed a complete factorization theory for classes of functions meromorphic in the disk $|z|1$. Such a class $N\{\omega\}$ is associated with a given positive continuous function $\omega(x)$ on $[0,1)$ satisfying the conditions $\omega(0)=1$ and $\omega(x)\in L[0,1)$, contains an arbitrary function meromorphic in $|z|1$ for a suitable choice of $\omega(x)$, and coincides in the special case $\omega(x)\equiv1$ with the class $N$ of functions of bounded form of R. Nevanlinna ([2], Chapter VI). In this present paper we study boundary properties of the classes $N\{\omega\}$, which are contained in $N$ when $\omega(x)\uparrow+\infty$ as $x\uparrow1$. We will prove a number of theorems giving various refined metric characteristics of those exceptional sets $E\subset[0{,}2\pi]$ of measure zero on which a function in the class $N\{\omega\}\subset N$ may not possess a radial boundary value. A characteristic of the exceptional sets $E$ will be given in terms of the convex capacity $\operatorname{Cap}\{E;\lambda_n\}$ with respect to a sequence$\{\lambda_n\}$, the Hausdorff $h$-measure $m(E;h)$, or the measure $C_\omega(E)$ associated with the function $\omega(x)$ generating the given class $N\{\omega\}\subset N$. 
@article{IM2_1970_4_6_a5,
     author = {M. M. Dzhrbashyan and V. S. Zakharyan},
     title = {Boundary properties of subclasses of meromorphic functions of},
     journal = {Izvestiya. Mathematics},
     pages = {1273--1354},
     year = {1970},
     volume = {4},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_6_a5/}
}
TY  - JOUR
AU  - M. M. Dzhrbashyan
AU  - V. S. Zakharyan
TI  - Boundary properties of subclasses of meromorphic functions of
JO  - Izvestiya. Mathematics
PY  - 1970
SP  - 1273
EP  - 1354
VL  - 4
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IM2_1970_4_6_a5/
LA  - en
ID  - IM2_1970_4_6_a5
ER  - 
%0 Journal Article
%A M. M. Dzhrbashyan
%A V. S. Zakharyan
%T Boundary properties of subclasses of meromorphic functions of
%J Izvestiya. Mathematics
%D 1970
%P 1273-1354
%V 4
%N 6
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_6_a5/
%G en
%F IM2_1970_4_6_a5
M. M. Dzhrbashyan; V. S. Zakharyan. Boundary properties of subclasses of meromorphic functions of. Izvestiya. Mathematics, Tome 4 (1970) no. 6, pp. 1273-1354. http://geodesic.mathdoc.fr/item/IM2_1970_4_6_a5/

[1] Dzhrbashyan M. M., “Teoriya faktorizatsii funktsii, meromorfnykh v kruge”, Matem. sb., 79(121) (1969), 517–615 | Zbl

[2] Nevanlinna R., Odnoznachnye analiticheskie funktsii, gl. VI, Gostekhizdat, M., 1941 | MR

[3] Frostman O., “Sur les produits de Blaschke”, Fysiogr. Säldsk Lund, föhr., 12:15 (1939), 1–14 | MR

[4] Carleson L., On a Class of Meromorphic Functions and Its Associated Exceptional Sets, Thesis, Uppsala, 1950 | MR

[5] Zakharyan V. S., “O radialnykh predelnykh znacheniyakh odnogo klassa funktsii, meromorfnykh v kruge”, Izv. AN SSSR. Ser. matem., 27 (1963), 801–818 | Zbl

[6] Temko K. V., “Vypuklaya emkost i ryady Fure”, Dokl. AN SSSR, 110:6 (1956), 943–944 ; РЈС‡. зап. МГУ, 186 (1959), 83–108 | MR | Zbl | MR | Zbl

[7] Temko K. V., “O vypukloi emkosti”, Matem. sb., 51(93) (1960), 217–226 | MR

[8] Bari N. K., Trigonometricheskie ryady, gl. V, § 12, Fizmatgiz, M., 1961 | MR

[9] Zigmund A., Trigonometricheskie ryady, t. II, gl. XIII, Mir, M., 1965 | MR

[10] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, gl. IX, Nauka, M., 1966

[11] Dzhrbashyan M. M., “O kanonicheskom predstavlenii meromorfnykh v edinichnom kruge funktsii”, Dokl. AN ArmSSR, 3:1 (1945), 3–9; “Рљ РїСЂРѕР±Р»РμРјРμ РїСЂРμдставимости аналитичРμСЃРєРёС... функциРNo”, РЎРѕРѕР±С‰. Р�РЅ-та матРμРј. Рё РјРμС.... РђРќ РђСЂРјРЎРЎР , 1948, No 2, 3–40

[12] Dzhrbashyan M. M., Zakharyan V. S., “O granichnykh svoistvakh meromorfnykh funktsii klassa $N_\alpha$”, Dokl. AN SSSR, 173:6 (1967), 1247–1250 | Zbl

[13] Dzhrbashyan M. M., “Obobschennyi operator Rimana–Liuvillya i nekotorye ego primeneniya”, Izv. AN SSSR. Ser. matem., 32 (1968), 1075–1111 | Zbl

[14] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, t. II, Nauka, M., 1966, 617–620

[15] Zakharyan V. S., “O radialnykh predelnykh znacheniyakh funktsii $B_\alpha$”, Izv. AN ArmSSR, 3:4–5 (1968), 287–300 | Zbl