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PreprintCC BY 4.0arXiv

Refined Bohr Inequalities and Bohr Radii Involving Schwarz Mappings for Holomorphic Functions in Banach Spaces and JB*-Triples

  • Nabadwip Sarkar
  • Pradip Das
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Abstract

In this paper, we investigate refined Bohr-type inequalities involving Schwarz mappings for holomorphic mappings defined on the unit ball BX of a complex Banach space. We first establish refined Bohr inequalities for scalar-valued holomorphic mappings F : BX → 𝕌. We then extend some results to vector-valued holomorphic mappings involving Schwarz mappings of the form F : BX → 𝕌̅ n, n ≥ 2, where improved Bohr radii are obtained under suitable norm conditions. Furthermore, we study the Bohr radius involving Schwarz mappings for holomorphic mappings whose ranges are contained in the closure of the unit ball of a JB*-triple. Our results generalize the results of Jia \textit{et al.} \cite{JLP}, Liu \textit{et al.} \cite{LLP2021} and Liu \textit{et al.} \cite{LSX2018}.

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Cite

BibTeXRIS
BibTeX
@misc{sarkar2026refined,
  title = {{Refined Bohr Inequalities and Bohr Radii Involving Schwarz Mappings for Holomorphic Functions in Banach Spaces and JB*-Triples}},
  author = {Nabadwip Sarkar and Pradip Das},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02935},
  eprint = {2610.02935},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02935},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Refined Bohr Inequalities and Bohr Radii Involving Schwarz Mappings for Holomorphic Functions in Banach Spaces and JB*-Triples
AU  - Nabadwip Sarkar
AU  - Pradip Das
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.02935
UR  - https://arxiv.org/abs/2610.02935
AB  - In this paper, we investigate refined Bohr-type inequalities involving Schwarz mappings for holomorphic mappings defined on the unit ball B_X of a complex Banach space. We first establish refined Bohr inequalities for scalar-valued holomorphic mappings F : B_X → 𝕌. We then extend some results to vector-valued holomorphic mappings involving Schwarz mappings of the form F : B_X → 𝕌̅^ n, n ≥ 2, where improved Bohr radii are obtained under suitable norm conditions. Furthermore, we study the Bohr radius involving Schwarz mappings for holomorphic mappings whose ranges are contained in the closure of the unit ball of a JB^*-triple. Our results generalize the results of Jia \textit{et al.} \cite{JLP}, Liu \textit{et al.} \cite{LLP2021} and Liu \textit{et al.} \cite{LSX2018}.
ER  -