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Bohr-type inequalities for unimodular bounded analytic functions

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arxiv 2302.07745 v1 pith:2PLGDTHH submitted 2023-02-15 math.CV

classification math.CV
keywords functionsanalyticbohr-typeboundedinequalitiesinftyseveralvarphi
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abstract

In this paper, we establish several new versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing $\varphi=\{\varphi_n(r)\}^{\infty}_{n=0}$ in place of the $\{r^n\}^{\infty}_{n=0}$ in the power series representations of the functions involved with the Bohr sum and thereby introducing a single parameter, which generalize several related results of earlier authors.

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