Multidimensional analogues of refined Bohr’s inequality

Liu, Ming-Sheng; Ponnusamy, Saminathan

doi:10.1090/proc/15371

Multidimensional analogues of refined Bohr’s inequality
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by Ming-Sheng Liu and Saminathan Ponnusamy PDF

Proc. Amer. Math. Soc. 149 (2021), 2133-2146 Request permission

Abstract:

In this paper, we first establish a version of multidimensional analogues of the refined Bohr’s inequality. Then we establish two versions of multidimensional analogues of improved Bohr’s inequality with initial coefficient being zero. Finally we establish two versions of multidimensional analogues of improved Bohr’s inequality with the initial coefficient being replaced by absolute value of the function, and to prove that most of the results are sharp.

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