  We consider the embedding of integrable Teichm\"uller spaces $T_p$ into
analytic Besov spaces by using pre-Schwarzian derivatives. Unlike the case of
the Bers embedding by Schwarzian derivatives, there is a big difference between
the cases $p>1$ and $p=1$. In this paper, we focus on the case $p=1$ and
generalize the previous results obtained for $p>1$. This gives a unified
approach to the complex analytic theory of integrable Teichm\"uller spaces
$T_p$ for all $p \geq 1$.
