Geodesic
Inequalities for majorizing analytical functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 155-173 
A. V. Olesov. Inequalities for majorizing analytical functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 155-173. http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a9/
@article{ZNSL_2004_314_a9,
     author = {A. V. Olesov},
     title = {Inequalities for majorizing analytical functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {155--173},
     year = {2004},
     volume = {314},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a9/}
}
TY  - JOUR
AU  - A. V. Olesov
TI  - Inequalities for majorizing analytical functions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 155
EP  - 173
VL  - 314
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a9/
LA  - ru
ID  - ZNSL_2004_314_a9
ER  - 
%0 Journal Article
%A A. V. Olesov
%T Inequalities for majorizing analytical functions
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 155-173
%V 314
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a9/
%G ru
%F ZNSL_2004_314_a9

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For analytic functions satisfying Meyman's majorization conditions, with the use of classical properties of conformal mappings exact inequalities complementing and strengthening the results of Akhiezer and Meyman are derived. As a corollary, for the modulus of the derivative of a rationally-trigonometric function a Bernstein type bound, which implies the result by Borwein, Erdélyi, and Zhang, is obtained.

[1] N. N. Meiman, “Differentsialnye neravenstva i nekotorye voprosy raspredeleniya nulei tselykh i odnoznachnykh analiticheskikh funktsii”, Uspekhi mat. nauk, 7:3 (1952), 3–62 | MR | Zbl

[2] N. I. Akhiezer, Lektsii po teorii approksimatsii, M., 1965

[3] V. N. Dubinin, “O primenenii konformnykh otobrazhenii v neravenstvakh dlya ratsionalnykh funktsii”, Izv. RAN, ser. mat., 66:2 (2002), 67–80 | MR | Zbl

[4] P. Borwein, T. Erdelyi, J. Zhang, “Chebyshev polynomials and Markov–Bernstein type inequalities for the rational spaces”, J. London Math. Soc., 50 (1994), 501–519 | MR | Zbl

[5] S. B. Stechkin, “Obobschenie nekotorykh neravenstv S. N. Bernshteina”, Dokl. AN SSSR, 60:9 (1948), 1511–1514 | Zbl

[6] V. N. Dubinin, “Teoremy iskazheniya dlya polinomov na okruzhnosti”, Mat. sb., 191:12 (2000), 51–60 | MR | Zbl

[7] V. N. Dubinin, “Konformnye otobrazheniya i neravenstva dlya algebraicheskikh polinomov”, Algebra i analiz, 13:5 (2001), 16–43 | MR | Zbl

[8] U. Kheiman, P. Kennedi, Subgarmonicheskie funktsii, M., 1980

[9] N. A. Lebedev, “Nekotorye otsenki dlya funktsii, regulyarnykh i odnolistnykh v kruge”, Vestn. LGU, ser. mat., fiz., khim., 11:4 (1955), 3–21 | Zbl

[10] N. A. Lebedev, Printsip ploschadei v teorii odnolistnykh funktsii, M., 1975 | MR