涉及与巴拿赫空间中全纯映射相关的弗雷歇导数的改进玻尔不等式
Improved Bohr inequalities involving Fréchet derivatives associated with Holomorphic mappings in Banach spaces
- Amity School of Applied Sciences, Amity University Mumbai（孟买阿美提大学应用科学学院）
- Department of Mathematics, Raiganj University（拉根杰大学数学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究复巴拿赫空间中与施瓦茨函数相关全纯映射的玻尔现象，通过建立涉及高阶弗雷歇导数的尖锐玻尔型不等式确定玻尔半径，为相关问题提供肯定答案并扩展经典不等式到巴拿赫空间全纯映射情形。
AI中文摘要：
受导数玻尔不等式及其改进的最新进展的启发，我们研究了与施瓦茨函数相关的复巴拿赫空间中全纯映射的玻尔现象。我们建立了关于\(|F(z)|\)及其改进形式\(|F(z)|^2\)的涉及高阶弗雷歇导数的尖锐玻尔型不等式。确定了相应的玻尔半径并证明是最优的。我们的结果为问题1.1和1.2提供了肯定答案，并将几个经典和最近的玻尔不等式从单位圆盘扩展到巴拿赫空间上全纯映射的情形。
英文摘要：
Motivated by recent advances in derivative Bohr inequalities and their refinements, we investigate the Bohr phenomenon for holomorphic mappings in complex Banach spaces associated with Schwarz functions. We establish sharp Bohr-type inequalities involving higher-order Fréchet derivatives for both $|F(z)|$ and its refined counterpart $|F(z)|^2$. The corresponding Bohr radii are determined and shown to be best possible. Our results provide affirmative answers to Questions 1.1 and 1.2 and extend several classical and recent Bohr inequalities from the unit disk to the setting of holomorphic mappings on Banach spaces.
