Hölder Spaces on Closed Curves
- Authors: Kats B.A.1, Skvortsova G.S.1
-
Affiliations:
- Kazan (Volga Region) Federal University
- Issue: Vol 39, No 9 (2018)
- Pages: 1362-1366
- Section: Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
- URL: https://journals.rcsi.science/1995-0802/article/view/203327
- DOI: https://doi.org/10.1134/S1995080218090391
- ID: 203327
Cite item
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
About the authors
B. A. Kats
Kazan (Volga Region) Federal University
Author for correspondence.
Email: katsboris877@gmail.com
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008
G. Sh. Skvortsova
Kazan (Volga Region) Federal University
Email: katsboris877@gmail.com
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008