An abstract approach to Bohr’s phenomenon

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Bohr Inequality for Odd Analytic Functions (2017, unknown): “ over the interval [0,1]. We see that ψhas two critical points and obtain that the maximum occurs when x1 = 1− √ 1− α2 √ 2 1 α , α≥ 1 3 , and thus, ψ(x) ≤ ψ(x1). Consequently, by (5), we ﬁnd that (6) X∞ k=0 |apk+1|r pk+1 ≤ 1 rp−1 3− 2 √ 2 √ 1−r2p = 1. Case 2: a<rp. In this case we set ρ= 1/ra”
Bohr phenomenon for certain subclasses of harmonic mappings (2020, background): “The interests in the Bohr phenomenon was revived in the 1990s due to the extensions to holomorphic function in C and to abstract setting [4].”
Remarks on the Bohr Phenomenon (2004, background): “[1, 2, 3 , 5]) have studied Bohr phenomena in Cn and also for various bases”