Geodesic
Necessary and sufficient conditions for the existence of boundary values of the modulus of a~function that is bounded and analytic in a~half-plane
Izvestiya. Mathematics , Tome 25 (1985) no. 1, pp. 89-114.

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

Necessary and sufficient conditions are obtained for the existence of a nontangential limit and of a limit along the normal at a particular point of the boundary for the modulus of a function that is bounded and analytic in a half-plane; the conditions consist in the existence at this point of the derivative and of the symmetric derivative, respectively, of the mass distribution function. Bibliography: 14 titles 
@article{IM2_1985_25_1_a5,
     author = {A. P. Mul},
     title = {Necessary and sufficient conditions for the existence of boundary values of the modulus of a~function that is bounded and analytic in a~half-plane},
     journal = {Izvestiya. Mathematics },
     pages = {89--114},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_25_1_a5/}
}
TY  - JOUR
AU  - A. P. Mul
TI  - Necessary and sufficient conditions for the existence of boundary values of the modulus of a~function that is bounded and analytic in a~half-plane
JO  - Izvestiya. Mathematics 
PY  - 1985
SP  - 89
EP  - 114
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1985_25_1_a5/
LA  - en
ID  - IM2_1985_25_1_a5
ER  - 
%0 Journal Article
%A A. P. Mul
%T Necessary and sufficient conditions for the existence of boundary values of the modulus of a~function that is bounded and analytic in a~half-plane
%J Izvestiya. Mathematics 
%D 1985
%P 89-114
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1985_25_1_a5/
%G en
%F IM2_1985_25_1_a5
A. P. Mul. Necessary and sufficient conditions for the existence of boundary values of the modulus of a~function that is bounded and analytic in a~half-plane. Izvestiya. Mathematics , Tome 25 (1985) no. 1, pp. 89-114. http://geodesic.mathdoc.fr/item/IM2_1985_25_1_a5/

[1] Duren P. L., Theory of $H^p$-spaces, New York, 1970, 258 pp. | MR

[2] Kollingvud E., Lovater A., Teoriya predelnykh mnozhestv, Mir, M., 1971 | MR

[3] Tanaka Chuji, “On the boundary values of Blaschke products and their quotients”, Proc. Amer. Math. Soc., 14:3 (1963), 472 | DOI | MR | Zbl

[4] Nosiro K., Predelnye mnozhestva, IL, M., 1963

[5] Cargo G. T., “The boundary behavior of Blaschke products”, Math. Anal. and Appl., 5 (1962), 1–16 | DOI | MR | Zbl

[6] Ahern P. R., Clark D. N., “Radial $N$-ih derivatives of Blaschke products”, Math. Scand., 28 (1971), 189–201 | MR | Zbl

[7] Atkinson F., Diskretnye i nepreryvnye granichnye zadachi, Mir, M., 1968 | MR | Zbl

[8] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956

[9] De Brein N. G., Asimptoticheskie metody v analize, IL, M., 1961

[10] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974

[11] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

[12] Govorov N. V., “Ob indikatore funktsii netselogo poryadka, analiticheskikh i vpolne regulyarnogo rosta v poluploskosti”, Dokl. AN SSSR, 162:3 (1965), 495–498 | MR | Zbl

[13] Govorov N. V., “Ob indikatore funktsii tselogo poryadka, analiticheskikh i vpolne regulyarnogo rosta v poluploskosti”, Dokl. AN SSSR, 172:14 (1967), 763–766 | MR | Zbl

[14] Grishin A. F., “O funktsiyakh, golomorfnykh vnutri ugla, imeyuschikh tam nulevoi poryadok”, Teoriya funktsii, funkts. analiz i ikh prilozheniya, 1965, no. 1, 41–56 | Zbl