Abstract In this paper, we first give the Bohr inequality of norm type for holomorphic mappings with lacunary series on the unit polydisk in C n under some restricted conditions. Next we also establish the Bohr inequality of norm type for holomorphic mappings with lacunary series on the unit ball of complex Banach spaces under some additional conditions, and the Bohr inequality of functional type for holomorphic mappings with lacunary series on the unit ball of complex Banach spaces. Our derived results reduce to the corresponding results in one complex variable.

中文翻译：

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几个复变量中具有空缺级数的全纯映射的玻尔不等式

摘要 在本文中，我们首先给出了C n 中单位多圆盘上具有空位级数的全纯映射的范数类型的玻尔不等式在一些限制条件下。接下来我们还建立了一些附加条件下复Banach空间单位球上有缺损级数的全纯映射的范数型玻尔不等式，以及复Banach空间单位球上缺损级数的全纯映射的泛函型玻尔不等式. 我们得出的结果简化为一个复杂变量中的相应结果。