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Regular version of the site

Article

Smoothness of a holomorphic function and its modulus on the boundary of a polydisk

Journal of Mathematical Sciences. 2018. Vol. 234. No. 3. P. 381-383.

We prove that if function f is holomorphic in the polydisk D^n, n≥2, f is continuous in D^n, f(z)≠0, z∈D^n, and f belongs to the α-Hölder class, 0<α<1, on the boundary of D^n, then f belongs to the α/2- Hölder class on D^n for any ε>0.