Geodesic
An estimate for the subharmonic difference of subharmonic functions. I
Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 191-218 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $u$, $v$ and $w=u-v$ be subharmonic functions in the half-plane $\Pi:\operatorname{Re}\omega>v$ and suppose that $u(\omega)$ and $v(\omega)$ are majorized by a positive function of the form $M(\omega)=\rho T(\rho,\tau)$, where $\rho=|\omega|$ and $\tau=1-\frac2\pi|\arg\omega|$. An inequality for the subharmonic difference $w=u-v$ is obtained in terms of the function $T(t,\tau)$, $0, $0<\tau<1$, which then gives an estimate for the difference from above. This inequality is carried over by conformal mappings to a class of regions with cusps (horn regions). Bibliography: 12 titles. 
@article{SM_1977_31_2_a4,
     author = {I. F. Krasichkov-Ternovskii},
     title = {An estimate for the subharmonic difference of subharmonic {functions.~I}},
     journal = {Sbornik. Mathematics},
     pages = {191--218},
     year = {1977},
     volume = {31},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_31_2_a4/}
}
TY  - JOUR
AU  - I. F. Krasichkov-Ternovskii
TI  - An estimate for the subharmonic difference of subharmonic functions. I
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 191
EP  - 218
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1977_31_2_a4/
LA  - en
ID  - SM_1977_31_2_a4
ER  - 
%0 Journal Article
%A I. F. Krasichkov-Ternovskii
%T An estimate for the subharmonic difference of subharmonic functions. I
%J Sbornik. Mathematics
%D 1977
%P 191-218
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1977_31_2_a4/
%G en
%F SM_1977_31_2_a4
I. F. Krasichkov-Ternovskii. An estimate for the subharmonic difference of subharmonic functions. I. Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 191-218. http://geodesic.mathdoc.fr/item/SM_1977_31_2_a4/

[1] M. L. Cartwright, “On analytic functions regular in the unit circle, I”, Quart. I. Math. Oxford ser., 4:16 (1933), 246–257 | Zbl

[2] C. N. Linden, “Functions regular in the unit circle”, Proc. Cambr. Phil. Soc., 52:1 (1956), 49–60 | DOI | MR | Zbl

[3] N. K. Nikolskii, “Odnostoronnie i modulnye otsenki funktsii, garmonicheskikh v kruge i polose”, DAN SSSR, 205:3 (1972), 18–21 | MR

[4] N. K. Nikolskii, Izbrannye zadachi vesovoi approksimatsii i spektralnogo analiza, Trudy Matem. in-ta im. V. A. Steklova, CXX, 1974 | MR

[5] V. I. Matsaev, “O roste tselykh funktsii, dopuskayuschikh nekotorye otsenki snizu”, DAN SSSR, 132:2 (1960), 283–286 | Zbl

[6] V. I. Matsaev, “Faktorizatsiya v nekotorykh klassakh funktsii”, Tezisy dokl. Vsesoyuzn. konf. po TFKP, Kharkov, 1971, 138–139

[7] L. Ahlfors, “Untersuchungen zur Theorie der konformen Abbildung und der ganzen Funktionen”, Acta Soc. Scient. fennica, ser. A, 1:9 (1930), 2–40 | Zbl

[8] S. E. Varshavskii, “Konformnye otobrazheniya beskonechnykh polos”, Matematika, 2:4 (1958), 67–116

[9] E. Kolligvud, A. Lovater, Teoriya predelnykh mnozhestv, izd-vo «Mir», Moskva, 1971 | MR

[10] M. A. Evgrafov, Analiticheskie funktsii, izd-vo «Nauka», Moskva, 1968 | MR

[11] R. Nevanlinna, Odnoznachnye analiticheskie funktsii, OGIZ, Moskva–Leningrad, 1941

[12] I. I. Privalov, Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, Moskva–Leningrad, 1950