Recently, there has been a number of good deal of research on the Bohr’s phenomenon in various settings including a refined formulation of his classical version of the inequality. Among them, in Paulsen et al. (Proc Lond Math Soc 85(2):493–512, 2002) the authors considered cases in which the above functions have a multiple zero at the origin. In this article, we present a refined version of Bohr’s inequality for these cases and give a partial answer to a question from Paulsen et al. (2002) for the revised setting.

中文翻译：

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原点具有多个零的函数的玻尔类型不等式

最近，在各种环境下对玻尔现象进行了大量的研究，包括对他的不等式的经典形式的提炼。其中，在Paulsen等。（Proc Lond Math Soc 85（2）：493–512，2002）作者考虑了上述函数在原点具有多个零的情况。在本文中，我们为这些情况提供了玻尔不等式的精简版本，并部分回答了保尔森等人的问题。（2002年）进行修改。