170
Views
1
CrossRef citations to date
0
Altmetric
Articles

Bohr's phenomenon for holomorphic and harmonic functions with lacunary series in complex Banach spaces

ORCID Icon
Pages 492-503 | Received 17 Sep 2022, Accepted 02 Nov 2022, Published online: 21 Dec 2022

References

  • Bohr H. A theorem concerning power series. Proc London Math Soc. 1914;13(2):1–5.
  • Abu-Muhanna Y. Bohr's phenomenon in subordination and bounded harmonic classes. Complex Var Elliptic Equ. 2010;55(11):1071–1078.
  • Alkhaleefah SA, Kayumov IR, Ponnusamy S. On the Bohr inequality with a fixed zero coefficient. Proc Amer Math Soc. 2019;147(12):5263–5274.
  • Allu V, Arora V. Bohr–Rogosinski type inequalities for concave univalent functions, Preprint. arXiv:2204.14085.
  • Kayumov IR, Ponnusamy S. Bohr inequality for odd analytic functions. Comput Methods Funct. 2017;17:679–688.
  • Kayumov IR, Ponnusamy S. Bohr's inequalities for analytic functions with lacunary series and harmonic functions. J Math Anal Appl. 2018;465:857–871.
  • Kayumov IR, Ponnusamy S. On a powered Bohr inequality. Ann Acad Sci Fenn Ser A I Math. 2019;44:301–310.
  • Kumar S, Sahoo SK. A generalization of the Bohr–Rogosinski sum, Preprint. arXiv:2106.06502.
  • Abu-Muhanna Y, Ali RM, Ponnusamy S. On the Bohr inequality. In: Govil NK, et al., editors. Progress in approximation theory and applicable complex analysis. Springer Optimization and Its Applications; Vol. 117, 2016. p. 265–295.
  • Dixon PG. Banach algebras satisfying the non-unital von Neumann inequality. Bull Lond Math Soc. 1995;27:359–362.
  • Boas HP, Khavinson D. Bohr's power series theorem in several variables. Proc Amer Math Soc. 1997;125:2975–2979.
  • Aizenberg L. Multidimensional analogues of Bohr's theorem on power series. Proc Amer Math Soc. 2000;128(4):1147–1155.
  • Liu MS, Ponnusamy S. Multidimensional analogues of refined Bohr's inequality. Proc Amer Math Soc. 2021;149:2133–2146.
  • Hamada H, Honda T, Kohr G. Bohr's theorem for holomorphic mappings with the values in homogeneous balls. Isr J Math. 2009;173:177–187.
  • Bhowmik B, Das N. Bohr radius and its asymptotic value for holomorphic functions in higher dimensions. C R Math Acad Sci Paris. 2021;359:911–918.
  • Arora V, Kumar S. Bohr's phenomenon in complex Banach space, Preprint. arxiv.org/abs/2205.07111.
  • Aizenberg L. Generalization of results about the Bohr radius for power series. Stud Math. 2007;180:161–168.
  • Aizenberg L. Remarks on the Bohr and Rogosinski phenomena for power series. Anal Math Phys. 2012;2(1):69–78.
  • Boas HP. Majorant series. J Korean Math Soc. 2000;37:321–337.
  • Defant A, Frerick L. A logarithmic lower bound for multi-dimensional Bohr radii. Isr J Math. 2006;152:17–28.
  • Dineen S, Timoney RM. Absolute bases, tensor products and a theorem of Bohr. Studia Math. 1989;94:227–234.
  • Ali RM, Barnard RW, Solynin AY. A note on Bohr's phenomenon for power series. J Math Anal Appl. 2017;449:154–167.
  • Liu X, Liu T. The Bohr inequality for holomorphic mappings with lacunary series in several complex variables. J Math Anal Appl. 2020;485(2):123844.
  • Kayumov IR, Ponnusamy S, Shakirov N. Bohr radius for locally univalent harmonic mappings. Math Nachr. 2017;291:1757–1768.
  • Liu Z, Ponnusamy S. Bohr radius for subordination and K-quasiconformal harmonic mappings. Bull Malays Math Sci Soc. 2019;42:2151–2168.
  • Liu MS, Ponnusamy S, Wang J. Bohr's phenomenon for the classes of Quasi-subordination and K-quasiregular harmonic mappings. Rev R Acad Cienc Exactas Fís Nat Ser A Mat. 2020;114:1–15.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.