The Bohr-Type Inequalities for Holomorphic Mappings with a Lacunary Series in Several Complex Variables

In this paper, we mainly use the Fréchet derivative to extend the Bohr inequality with a lacunary series to the higher-dimensional space, namely, mappings from Un to U (resp. Un to Un). In addition, we discuss whether or not there is a constant term in f, and we obtain two redefined Bohr inequalities in Un. Finally, we redefine the Bohr inequality of the odd and even terms of the analytic function f so as to obtain conclusions for two different higher-dimensional alternating series.