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PreprintCC BY 4.0arXiv

Improved Bohr-Rogosinski radius for holomorphic mappings with values in complex Banach spaces

  • Luyi Zeng
  • Liangpeng Xiong
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Abstract

In this paper, we extend some Bohr-Rogosinski type inequalities of analytic functions in ℂ to the cases of holomorphic mappings with values in higher-dimensional complex space. First, we obtain the general Bohr-Rogosinski radius for holomorphic mappings with values in the closure of the unit polydisc in ℂ n. Furthermore, we consider the corresponding problems for holomorphic mappings with value in the closure of the unit ball of a JB*-triple. All the radius are optimal.

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Cite

BibTeXRIS
BibTeX
@misc{zeng2026improved,
  title = {{Improved Bohr-Rogosinski radius for holomorphic mappings with values in complex Banach spaces}},
  author = {Luyi Zeng and Liangpeng Xiong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.28357},
  eprint = {2609.28357},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28357},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Improved Bohr-Rogosinski radius for holomorphic mappings with values in complex Banach spaces
AU  - Luyi Zeng
AU  - Liangpeng Xiong
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.28357
UR  - https://arxiv.org/abs/2609.28357
AB  - In this paper, we extend some Bohr-Rogosinski type inequalities of analytic functions in ℂ to the cases of holomorphic mappings with values in higher-dimensional complex space. First, we obtain the general Bohr-Rogosinski radius for holomorphic mappings with values in the closure of the unit polydisc in ℂ ^n. Furthermore, we consider the corresponding problems for holomorphic mappings with value in the closure of the unit ball of a JB^*-triple. All the radius are optimal.
ER  -