Analytic Besov functions, pre-Schwarzian derivatives, and integrable Teichm\"uller spaces

Abstract

We study the embedding of integrable Teichm\"uller spaces $T_p$ into analytic Besov spaces via pre-Schwarzian derivatives. In contrast to the Bers embedding by Schwarzian derivatives, a significant difference arises between the cases $p>1$ and $p=1$. In this paper we focus on the case $p=1$ and extend previous results obtained for $p>1$. This provides a unified framework for the complex-analytic theory of integrable Teichm\"uller spaces $T_p$ for all $p \geq 1$.