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Journal of Mathematical Sciences

, Volume 229, Issue 5, pp 568–571 | Cite as

Smoothness of a Holomorphic Function in a Ball and of its Modulus on the Sphere

  • N. A. ShirokovEmail author
Article
  • 13 Downloads

Let a function f be holomorphic in the unit ball 𝔹 n , continuous in the closed ball \( {\overline{\mathbb{B}}}^n \) , and let f(z) ≠ 0, z ∈ 𝔹 n . Assume that |f| belongs to the α-Hölder class on the unit sphere S n , 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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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