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 $U^n$ to $U$ (resp. $U^n$ to $U^n$). In addition, we discuss whether or not there is a constant term in $f$, and we obtain two redefined Bohr inequalities in $U^n$. 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.
Rouyuan Lin
,
Mingsheng Liu
,
Saminathan Ponnusamy
. THE BOHR-TYPE INEQUALITIES FOR HOLOMORPHIC MAPPINGS WITH A LACUNARY SERIES IN SEVERAL COMPLEX VARIABLES*[J]. Acta mathematica scientia, Series B, 2023
, 43(1)
: 63
-79
.
DOI: 10.1007/s10473-023-0105-8
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