Analogue of Kellogg’s Theorem for Piecewise Lyapunov Domains

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Abstract

In weighted Hölder spaces, classes of smooth arcs and piecewise smooth contours are introduced that are invariant under power mappings. The boundary properties of conformal mappings are described in terms of these classes by analogy with Kellogg’s classical theorem.

About the authors

A. P. Soldatov

Federal Research Center “Computer Science and Control,” Russian Academy of Sciences; Moscow Center of Fundamental and Applied Mathematics, Lomonosov Moscow State University, Moscow, Russia; National Research University “Moscow Power Engineering Institute”

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Email: soldatov48@gmail.com
119333, Moscow, Russia; 111250, Moscow, Russia

References

  1. Голузин Г.М. Геометрическая теория функций комплексного переменного. М.: Наука, 1972.
  2. Векуа И.Н. Обобщенные аналитические функции. 2-е изд., М.: Наука, 1988.
  3. Солдатов А.П. Сингулярные интегральные операторы и эллиптические краевые задачи // Современ. математика. Фундамент. направления. 2017. Т. 63. С. 1–189.

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