Bohr inequalities for holomorphic mappings in higher-dimensional complex Banach spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908671516082176 |
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| author | Allu, Vasudevarao Biswas, Raju Mandal, Rajib |
| author_facet | Allu, Vasudevarao Biswas, Raju Mandal, Rajib |
| contents | In this paper, we investigates the Bohr phenomenon for holomorphic mappings $F$ from the unit ball $\mathbb{B}_X$ of a complex Banach space $X$ into the closure of the unit polydisc $\mathbb{D}^m$ within the space $\mathbb{C}^m$. First, we prove an improved Bohr inequality involving the squared norms of the mapping and its homogeneous expansions. Second, we derive a refined Bohr inequality that incorporates a combination of the coefficient norms and their squares. Finally, we obtain a refined Bohr inequality for compositions $F\circ ν$, where $ν$ is a Schwarz mapping with a zero of order $k$ at the origin. For each result, we demonstrate that the derived Bohr radius is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bohr inequalities for holomorphic mappings in higher-dimensional complex Banach spaces Allu, Vasudevarao Biswas, Raju Mandal, Rajib Complex Variables 32A05, 32A10, 32K05, 32M15 In this paper, we investigates the Bohr phenomenon for holomorphic mappings $F$ from the unit ball $\mathbb{B}_X$ of a complex Banach space $X$ into the closure of the unit polydisc $\mathbb{D}^m$ within the space $\mathbb{C}^m$. First, we prove an improved Bohr inequality involving the squared norms of the mapping and its homogeneous expansions. Second, we derive a refined Bohr inequality that incorporates a combination of the coefficient norms and their squares. Finally, we obtain a refined Bohr inequality for compositions $F\circ ν$, where $ν$ is a Schwarz mapping with a zero of order $k$ at the origin. For each result, we demonstrate that the derived Bohr radius is sharp. |
| title | Bohr inequalities for holomorphic mappings in higher-dimensional complex Banach spaces |
| topic | Complex Variables 32A05, 32A10, 32K05, 32M15 |
| url | https://arxiv.org/abs/2511.18953 |