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

TL;DR

This paper explores the embedding of integrable Teichmüller spaces into Besov spaces using pre-Schwarzian derivatives, highlighting differences between cases p>1 and p=1, and extending previous results for p=1.

Contribution

It provides a unified complex-analytic framework for all integrable Teichmüller spaces T_p with p ≥ 1, focusing on the p=1 case.

Findings

Extended results for p=1 case of T_p spaces

Identified differences between p>1 and p=1 cases

Unified the theory for all p ≥ 1

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 $p \geq 1$.