On the Young Conjugate Functions and the Behavior of the Maximal Terms of the Derivatives of Dirichlet Series
Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 74-81
Cet article a éte moissonné depuis la source Math-Net.Ru
We obtain a criterion for the growth of the maximal term of the Dirichlet series with positive exponents in terms of the behavior of the maximal terms of the successive derivatives of this series. This criterion is obtained from a more general result concerning Young conjugate functions proved in this paper.
@article{MZM_2001_69_1_a5,
author = {Ya. V. Mikityuk and M. N. Sheremeta and O. M. Sumyk},
title = {On the {Young} {Conjugate} {Functions} and the {Behavior} of the {Maximal} {Terms} of the {Derivatives} of {Dirichlet} {Series}},
journal = {Matemati\v{c}eskie zametki},
pages = {74--81},
year = {2001},
volume = {69},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a5/}
}
TY - JOUR AU - Ya. V. Mikityuk AU - M. N. Sheremeta AU - O. M. Sumyk TI - On the Young Conjugate Functions and the Behavior of the Maximal Terms of the Derivatives of Dirichlet Series JO - Matematičeskie zametki PY - 2001 SP - 74 EP - 81 VL - 69 IS - 1 UR - http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a5/ LA - ru ID - MZM_2001_69_1_a5 ER -
%0 Journal Article %A Ya. V. Mikityuk %A M. N. Sheremeta %A O. M. Sumyk %T On the Young Conjugate Functions and the Behavior of the Maximal Terms of the Derivatives of Dirichlet Series %J Matematičeskie zametki %D 2001 %P 74-81 %V 69 %N 1 %U http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a5/ %G ru %F MZM_2001_69_1_a5
Ya. V. Mikityuk; M. N. Sheremeta; O. M. Sumyk. On the Young Conjugate Functions and the Behavior of the Maximal Terms of the Derivatives of Dirichlet Series. Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 74-81. http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a5/
[1] Sheremeta M. N., “O posledovatelnostyakh maksimalnykh chlenov i tsentralnykh pokazatelei proizvodnykh ryadov Dirikhle”, Matem. zametki, 63:3 (1998), 457–467 | MR | Zbl
[2] Sheremeta M. N., Fedynyak S. I., “O proizvodnoi ryada Dirikhle”, Sib. matem. zh., 39:1 (1998), 206–223 | MR | Zbl
[3] Young W. H., “On classes of summable functions and their Fourier series”, Proc. Roy. Soc. (A), 87 (1912), 225–229 | DOI
[4] Evgrafov M. A., Asimptoticheskie otsenki i tselye funktsii, Fizmatgiz, M., 1962
[5] Bratischev A. V., “Ob obraschenii pravila Lopitalya”, Mekhanika sploshnoi sredy, Izd. RGU, Rostov-na-Donu, 1985, 28–42