Hölder Spaces on Closed Curves

Abstract

© 2018, Pleiades Publishing, Ltd. 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 Hν+(Γ),Hν−(Γ) 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.