$p$-Dirichlet spaces over chord-arc domains
$p$-Dirichlet spaces over chord-arc domains
Let $\Gamma$ be a rectifiable Jordan curve in the complex plane, $\Omega_i$ and $\Omega_e$ respectively the interior and exterior domains of $\Gamma$, and $p\geq 2$. Let $E$ be the vector space of functions defined on $\Gamma$ consisting of restrictions to $\Gamma$ of functions in $C^1(\mathbb C)$. We define three semi-norms …