AI 中文总结
该研究将单位圆盘上的Bohr型不等式推广至复Banach空间全纯映射情形，利用Fréchet导数等工具得到显式精确Bohr半径，还证明了含导数、系数与面积项的精细不等式的对应半径为指定方程的唯一正解。
AI 中文摘要
我们建立了从复Banach空间单位球到闭单位圆盘的全纯映射的新Bohr型不等式。利用Fréchet导数、指定阶的Schwarz映射与面积泛函，我们得到了由显式方程刻画的精确Bohr半径。我们进一步证明了一个包含导数项、系数项与面积项的精细Bohr不等式，并证明相应半径是方程$r^m=(\u221a17-3)/4$的唯一正解。我们还证明了所得半径与常数的精确性。我们的结果将近期若干关于单位圆盘上有界解析函数的Bohr型不等式推广到了复Banach空间上的全纯映射情形。
英文摘要
We establish new Bohr-type inequalities for holomorphic mappings from the unit ball of a complex Banach space into the closed unit disk. Using Fréchet derivatives, Schwarz mappings of prescribed orders and area functionals, we obtain sharp Bohr radii characterized by explicit equations. We further prove a refined Bohr inequality involving derivative, coefficient and area terms and show that the corresponding radius is the unique positive solution of $r^m=(\sqrt{17}-3)/4$. The sharpness of the obtained radii and constants is also established. Our results extend several recent Bohr-type inequalities for bounded analytic functions on the unit disk to the setting of holomorphic mappings on complex Banach spaces.
