Conformally Invariant Besov Spaces on Chord-Arc Domains

Inspired by the classical Besov $p$-space ($1<p<\infty$) defined by means of higher-order derivatives on the upper half-plane, we introduce Besov-type spaces on simply connected domains. We study the relation between the geometric properties of the domain and these spaces, and characterize chord-arc domains in terms of the isomorphisms among these Besov spaces. Furthermore, we obtain that these spaces on chord-arc domains inherit the conformal invariance from the classical setting.