Conformally Invariant Besov Spaces on Chord-Arc Domains

Abstract

Let $\Gamma$ be a rectifiable Jordan curve. We introduce the associated Besov $p$-spaces on $\Gamma$ and in its complementary domains, and characterize chord-arc curves by the natural trace isomorphisms among these spaces. We prove the characterization for the previously unresolved range $1<p<2$, thereby extending the known results $p\ge 2$ to $1<p<\infty$. We further give an alternative proof for $p\ge 2$.