Email this article Smoothness of a Holomorphic Function and Its Modulus on the Boundary of a Polydisk
- Authors: Shirokov N.A.1,2
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Affiliations:
- St. Petersburg State University, St. Petersburg Branch of HSE University
- St. Petersburg Department of the Steklov Mathematical Institute
- Issue: Vol 234, No 3 (2018)
- Pages: 381-383
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241907
- DOI: https://doi.org/10.1007/s10958-018-4016-5
- ID: 241907
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Abstract
We prove that if a function f is holomorphic in the polydisk ????n, n ≥ 2, f is continuous in \( \overline{{\mathbb{D}}^n} \), f(z) ≠ 0, z ∈ ????n, and |f| belongs to the α-Hölder class, 0 < α < 1, on the boundary of ????n, then f belongs to the \( \left(\frac{\alpha }{2}-\varepsilon \right) \)-Hölder class on \( \overline{{\mathbb{D}}^n} \) for any ε > 0.
About the authors
N. A. Shirokov
St. Petersburg State University, St. Petersburg Branch of HSE University; St. Petersburg Department of the Steklov Mathematical Institute
Author for correspondence.
Email: nikolai.shirokov@gmail.com
Russian Federation, St. Petersburg; St. Petersburg
