Let a function f be holomorphic in the unit ball 𝔹n, continuous in the closed ball \( {\overline{\mathbb{B}}}^n \) , and let f(z) ≠ 0, z ∈ 𝔹n. Assume that |f| belongs to the α-Hölder class on the unit sphere Sn, 0 < α ≤ 1. The present paper is devoted to the proof of the statement that f belongs to the α/2-Hölder class on \( {\overline{\mathbb{B}}}^n \).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 447, 2016, pp. 123–128.
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Shirokov, N.A. Smoothness of a Holomorphic Function in a Ball and of its Modulus on the Sphere. J Math Sci 229, 568–571 (2018). https://doi.org/10.1007/s10958-018-3699-y
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DOI: https://doi.org/10.1007/s10958-018-3699-y