  Similarly to the Bers simultaneous uniformization, the product of the
$p$-Weil-Petersson Teichm\"uller spaces for $p \geq 1$ provides the coordinates
for the space of $p$-Weil-Petersson embeddings $\gamma$ of the real line
$\mathbb R$ into the complex plane $\mathbb C$. We prove the biholomorphic
correspondence from this space to the $p$-Besov space of $u=\log \gamma'$ on
$\mathbb R$ for $p>1$. From this fundamental result, several consequences
follow immediately which clarify the analytic structures concerning parameter
spaces of $p$-Weil-Petersson curves. In particular, it follows that the
correspondence of the Riemann mapping parameters to the arc-length parameters
keeping the images of curves is a homeomorphism with bi-real-analytic
dependence of change of parameters. This is a counterpart to a classical
theorem of Coifman and Meyer for chord-arc curves.
