Cauchy Integral, Fractional Sobolev Spaces and Chord-Arc Curves

Huaying Wei, Michel Zinsmeister

Let $\Gamma$ be a bounded Jordan curve and ${\Omega }_i,{\Omega }_e$ its two complementary components. For $s\in (0,1)$ we define ${\mathcal{H}}^s(\Gamma )$ as the set of functions $f:\Gamma \to \mathbb{C}$ having har…