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.
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Kats, B.A., Skvortsova, G.S. Hölder Spaces on Closed Curves. Lobachevskii J Math 39, 1362–1366 (2018). https://doi.org/10.1134/S1995080218090391
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DOI: https://doi.org/10.1134/S1995080218090391