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Regular version of the site

Article

Smoothness of a holomorphic function in a ball and its modulus on the sphere

Journal of Mathematical Sciences. 2018. Vol. 229. No. 5. P. 568-571.

Let a function f be holomorphic in the unit ball B^n , continuous in the closed ball 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 B^n.