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A strengthened contour-and-solid property for lipschitz functions and extension of the derivative to the boundary

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Seminar on Deformations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1165))

Abstract

A strengthened contour-and-solid property for Lipschitz functions is proved as a sharpening of a result of [4]. The property is then applied to generalize a theorem of [3] on continuous extension of the derivative of a function, holomorphic in an open set, to the boundary. (© Институт математихи AH YCCP, 1983, preprint 83.35).

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References

  1. HAYMAN, W.K. and P.B. KENNEDY, Subharmonic functions I Academic Press, London-New York-san Francisco 1976; Russian transl.: У. ХЕйМАН, П. КЕННЕДИ, Субгармонические функции, Иэд. "Мир", Москва 1980. (P. 244 in Engl. ed. corresponds to p. 262 in Russ. ed.)

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  2. NEVANLINNA, R., Uniformisierung (Grundlehren der math. Wissenschaften 64), Springer-Verlag, berlin-Göttingen-Heidelberg 1953; 2. Aufl., Berlin-Heidelberg-New York 1967; Russian transl.: Р. НЕВАН-ЛИННА, Униформиэация, Иэд. иностр. лит., Москва 1955. (Pp. 336–338 in Germ. eds. correspond to pp. 372–374 in Russ. ed.)

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  3. TAMRAZOV, P.M. [ТАМРАЗОВ, П.М.], Контурные и телесные структурные свойства голоморфных функций комплексного переменного, Успехи мат. наук 28, 1 (1973), 131–161.

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  4. —, Контурно-телесные свойства голоморфных функций и отображений, Препринт 83.33, Институт математики АН Украинской ССР, Киев 1983, 17 pp.

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  5. TSUJI, M., Potential theory in modern function theory, Maruzen Co., Tokyo 1959.

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Julian Ławrynowicz

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© 1985 Springer-Verlag

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Tamrazov, P.M. (1985). A strengthened contour-and-solid property for lipschitz functions and extension of the derivative to the boundary. In: Ławrynowicz, J. (eds) Seminar on Deformations. Lecture Notes in Mathematics, vol 1165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076162

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  • DOI: https://doi.org/10.1007/BFb0076162

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16050-2

  • Online ISBN: 978-3-540-39734-2

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