Geodesic
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 
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/
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Voir la notice de l'article provenant de 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.

[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