Hölder Spaces on Closed Curves

Abstract

Let Γ be a closed Jordan curve on the complex plane dividing it onto domains D⁺ and D₋, ∞ ∈ D⁻. The Hölder space H_v (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.