On the Bohr inequality for the Cesáro operator

Ilgiz R. Kayumov; Diana M. Khammatova; Saminathan Ponnusamy

doi:10.5802/crmath.80

Analyse complexe, Analyse fonctionnelle

On the Bohr inequality for the Cesáro operator

Ilgiz R. Kayumov ¹ ; Diana M. Khammatova ¹ ; Saminathan Ponnusamy ²

¹ Kazan Federal University, 420 008 Kazan, Russia
² Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India

Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 615-620.

Résumé

We investigate an analog of Bohr’s results for the Cesáro operator acting on the space of holomorphic functions defined on the unit disk. The asymptotical behaviour of the corresponding Bohr sum is also estimated.

Reçu le : 2019-01-01
Révisé le : 2020-05-26
Accepté le : 2020-05-26
Publié le : 2020-09-14

DOI : 10.5802/crmath.80

Classification : 30H05, 30A10, 30C80

Affiliations des auteurs :

Ilgiz R. Kayumov ¹ ; Diana M. Khammatova ¹ ; Saminathan Ponnusamy ²

¹ Kazan Federal University, 420 008 Kazan, Russia
² Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {On the {Bohr} inequality for the {Ces\'aro} operator},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {615--620},
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     volume = {358},
     number = {5},
     year = {2020},
     doi = {10.5802/crmath.80},
     language = {en},
}

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Ilgiz R. Kayumov; Diana M. Khammatova; Saminathan Ponnusamy. On the Bohr inequality for the Cesáro operator. Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 615-620. doi : 10.5802/crmath.80. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.80/

Bibliographie
Cité par

[1] Yusuf Abu-Muhanna; Rosihan M. Ali; Saminathan Ponnusamy On the Bohr inequality, Progress in Approximation Theory and Applicable Complex Analysis (Springer Optimization and Its Applications), Volume 117, Springer, 2016, pp. 265-295 | Zbl

[2] Rosihan M. Ali; Roger W. Barnard; Alexander Yu. Solynin A note on Bohr’s phenomenon for power series, J. Math. Anal. Appl., Volume 449 (2017) no. 1, pp. 154-167 | MR | Zbl

[3] Harald Bohr A theorem concerning power series, Proc. Lond. Math. Soc., Volume 13 (1914), pp. 1-5 | DOI | MR | Zbl

[4] Enrico Bombieri Sopra un teorema di H. Bohr e G. Ricci sulle funzioni maggioranti delle serie di potenze, Boll. Unione Mat. Ital., Volume 17 (1962), pp. 276-282 | MR | Zbl

[5] Enrico Bombieri; Jean Bourgain A remark on Bohr’s inequality, Int. Math. Res. Not., Volume 2004 (2004) no. 80, pp. 4307-4330 | DOI | MR | Zbl

[6] P. G. Dixon Banach algebras satisfying the non-unital von Neumann inequality, Bull. Lond. Math. Soc., Volume 27 (1995) no. 4, pp. 359-362 | DOI | MR | Zbl

[7] Plamen B. Djakov; M. S. Ramanujan A remark on Bohr’s theorem and its generalizations, J. Anal., Volume 8 (2000), pp. 65-77 | MR | Zbl

[8] Stephan Ramon Garcia; Javad Mashreghi; William T. Ross Finite Blaschke products and their connections, Springer, 2018 | Zbl

[9] Godfrey H. Hardy; John E. Littlewood Some properties of fractional integrals II, Math. Z., Volume 34 (1931), pp. 403-439 | DOI | MR | Zbl

[10] Ilgiz R. Kayumov; Saminathan Ponnusamy Bohr inequality for odd analytic functions, Comput. Methods Funct. Theory, Volume 17 (2017) no. 4, pp. 679-688 | DOI | MR | Zbl

[11] Ilgiz R. Kayumov; Saminathan Ponnusamy Bohr’s inequalities for the analytic functions with lacunary series and harmonic functions, J. Math. Anal. Appl., Volume 465 (2018) no. 2, pp. 857-871 | DOI | MR | Zbl

[12] Ilgiz R. Kayumov; Saminathan Ponnusamy Improved version of Bohr’s inequality, C. R. Math. Acad. Sci. Paris, Volume 356 (2018) no. 3, pp. 272-277 | DOI | MR | Zbl

[13] Ilgiz R. Kayumov; Saminathan Ponnusamy On a powered Bohr inequality, Ann. Acad. Sci. Fenn., Math., Volume 44 (2019) no. 1, pp. 301-310 | DOI | MR | Zbl

[14] Johann von Neumann Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes, Math. Nachr., Volume 4 (1951), pp. 258-281 | MR | Zbl

[15] Krzysztof Stempak Cesáro averaging operators, Proc. R. Soc. Edinb., Sect. A, Math., Volume 124 (1994) no. 1, pp. 121-126 | DOI | MR | Zbl

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