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Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1362–1366 | Cite as

Hölder Spaces on Closed Curves

  • B. A. KatsEmail author
  • G. Sh. Skvortsova
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
  • 4 Downloads

Abstract

Let Γ be a closed Jordan curve on the complex plane dividing it onto domains D+ and D, ∞ ∈ D. The Hölder space Hv (Γ) is the space of functions satisfying the Hölder condition with exponent ν on Γ, and \(H^+_\nu(\Gamma),\;H^{-}_\nu(\Gamma)\) are its subspaces consisting of functions analytically extendable into D+ and D relatively. We study intersection and sum of these subspaces for nonsmooth and non-rectifiable curves.

Keywords and phrases

Hölder space non-smooth curves non-rectifiable curves 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

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