Refined Bohr inequalities and a refined Bohr-Rogosinski inequality on complex Banach spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914956881952768 |
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| author | Ahamed, Molla Basir Ahammed, Sabir Hamada, Hidetaka |
| author_facet | Ahamed, Molla Basir Ahammed, Sabir Hamada, Hidetaka |
| contents | In this paper, we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball $B_X$ of a complex Banach space $X$ into $\mathbb{C}$. As applications, we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball $B_X$ with values in higher dimensional spaces. Next, we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on $B_X.$ In addition, we establish an improved version of the Bohr inequality for holomorphic functions on $B_X$. All the results are proved to be sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Refined Bohr inequalities and a refined Bohr-Rogosinski inequality on complex Banach spaces Ahamed, Molla Basir Ahammed, Sabir Hamada, Hidetaka Complex Variables In this paper, we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball $B_X$ of a complex Banach space $X$ into $\mathbb{C}$. As applications, we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball $B_X$ with values in higher dimensional spaces. Next, we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on $B_X.$ In addition, we establish an improved version of the Bohr inequality for holomorphic functions on $B_X$. All the results are proved to be sharp. |
| title | Refined Bohr inequalities and a refined Bohr-Rogosinski inequality on complex Banach spaces |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2409.16610 |